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C2×D7945 #44541025

order31780
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15890
direct productC2×D7945
unambiguous semidirect product(C2×C5)⋊D1589
unambiguous semidirect product(C2×C7)⋊D1135
unambiguous semidirect product(C2×C227)⋊D35

Splittings

Fitting, socleC2×C5×C7×C227 ⋊ C2
derived, HallC5×C7×C227 ⋊ C22
HallC7×C227 ⋊ C2×D5
HallC5×C227 ⋊ C2×D7
SylowC227 ⋊ C2×D35
HallC5×C7 ⋊ C2×D227
SylowC7 ⋊ C2×D1135
SylowC5 ⋊ C2×D1589

Subgroups

subgroupG/H
center, hypercenterC2D7945
commutator, cosocle, hypocenterC5×C7×C227C22
FrattiniC1G
Fitting, socleC2×C5×C7×C227C2
LCSG ▷ C5×C7×C227
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 241
transitive degreeμt(G) = 15890

A minimal faithful permutation representation — 2 generators on 241 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241);(4,7)(5,6)(9,14)(10,13)(11,12)(16,241)(17,240)(18,239)(19,238)(20,237)(21,236)(22,235)(23,234)(24,233)(25,232)(26,231)(27,230)(28,229)(29,228)(30,227)(31,226)(32,225)(33,224)(34,223)(35,222)(36,221)(37,220)(38,219)(39,218)(40,217)(41,216)(42,215)(43,214)(44,213)(45,212)(46,211)(47,210)(48,209)(49,208)(50,207)(51,206)(52,205)(53,204)(54,203)(55,202)(56,201)(57,200)(58,199)(59,198)(60,197)(61,196)(62,195)(63,194)(64,193)(65,192)(66,191)(67,190)(68,189)(69,188)(70,187)(71,186)(72,185)(73,184)(74,183)(75,182)(76,181)(77,180)(78,179)(79,178)(80,177)(81,176)(82,175)(83,174)(84,173)(85,172)(86,171)(87,170)(88,169)(89,168)(90,167)(91,166)(92,165)(93,164)(94,163)(95,162)(96,161)(97,160)(98,159)(99,158)(100,157)(101,156)(102,155)(103,154)(104,153)(105,152)(106,151)(107,150)(108,149)(109,148)(110,147)(111,146)(112,145)(113,144)(114,143)(115,142)(116,141)(117,140)(118,139)(119,138)(120,137)(121,136)(122,135)(123,134)(124,133)(125,132)(126,131)(127,130)(128,129)

Conjugacy classes & character table

7948 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD31780
maximal normal subgroup ofD31780
maximal quotient ofDic15890, D31780

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31780, 27);