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C2×D7683 #44502252

order30732
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15366
direct productC2×D7683
unambiguous semidirect product(C2×C3)⋊D2561
unambiguous semidirect product(C2×C13)⋊D591
unambiguous semidirect product(C2×C197)⋊D39

Splittings

Fitting, socleC2×C3×C13×C197 ⋊ C2
derived, HallC3×C13×C197 ⋊ C22
HallC13×C197 ⋊ C2×D3
HallC3×C197 ⋊ C2×D13
SylowC197 ⋊ C2×D39
HallC3×C13 ⋊ C2×D197
SylowC13 ⋊ C2×D591
SylowC3 ⋊ C2×D2561

Subgroups

subgroupG/H
center, hypercenterC2D7683
commutator, cosocle, hypocenterC3×C13×C197C22
FrattiniC1G
Fitting, socleC2×C3×C13×C197C2
LCSG ▷ C3×C13×C197
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 215
transitive degreeμt(G) = 15366

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

Conjugacy classes & character table

7686 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD30732
maximal normal subgroup ofD30732
maximal quotient ofDic15366, D30732

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30732, 52);