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C2×D7761 #44526862

order31044
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15522
direct productC2×D7761
unambiguous semidirect product(C2×C3)⋊D2587
unambiguous semidirect product(C2×C13)⋊D597
unambiguous semidirect product(C2×C199)⋊D39

Splittings

Fitting, socleC2×C3×C13×C199 ⋊ C2
derived, HallC3×C13×C199 ⋊ C22
HallC13×C199 ⋊ C2×D3
HallC3×C199 ⋊ C2×D13
SylowC199 ⋊ C2×D39
HallC3×C13 ⋊ C2×D199
SylowC13 ⋊ C2×D597
SylowC3 ⋊ C2×D2587

Subgroups

subgroupG/H
center, hypercenterC2D7761
commutator, cosocle, hypocenterC3×C13×C199C22
FrattiniC1G
Fitting, socleC2×C3×C13×C199C2
LCSG ▷ C3×C13×C199
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 217
transitive degreeμt(G) = 15522

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

Conjugacy classes & character table

7764 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD31044
maximal normal subgroup ofD31044
maximal quotient ofDic15522, D31044

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31044, 76);