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C2×D7881 #44538638

order31524
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15762
direct productC2×D7881
unambiguous semidirect product(C2×C3)⋊D2627
unambiguous semidirect product(C2×C37)⋊D213
unambiguous semidirect product(C2×C71)⋊D111

Splittings

Fitting, socleC2×C3×C37×C71 ⋊ C2
derived, HallC3×C37×C71 ⋊ C22
HallC37×C71 ⋊ C2×D3
HallC3×C71 ⋊ C2×D37
HallC3×C37 ⋊ C2×D71
SylowC71 ⋊ C2×D111
SylowC37 ⋊ C2×D213
SylowC3 ⋊ C2×D2627

Subgroups

subgroupG/H
center, hypercenterC2D7881
commutator, cosocle, hypocenterC3×C37×C71C22
FrattiniC1G
Fitting, socleC2×C3×C37×C71C2
LCSG ▷ C3×C37×C71
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 113
transitive degreeμt(G) = 15762

A minimal faithful permutation representation — 2 generators on 113 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);(4,5)(7,42)(8,41)(9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(44,113)(45,112)(46,111)(47,110)(48,109)(49,108)(50,107)(51,106)(52,105)(53,104)(54,103)(55,102)(56,101)(57,100)(58,99)(59,98)(60,97)(61,96)(62,95)(63,94)(64,93)(65,92)(66,91)(67,90)(68,89)(69,88)(70,87)(71,86)(72,85)(73,84)(74,83)(75,82)(76,81)(77,80)(78,79)

Conjugacy classes & character table

7884 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD31524
maximal normal subgroup ofD31524
maximal quotient ofDic15762, D31524

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31524, 40);