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C2×D7843 #44535895

order31372
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15686
direct productC2×D7843
unambiguous semidirect product(C2×C11)⋊D713
unambiguous semidirect product(C2×C23)⋊D341
unambiguous semidirect product(C2×C31)⋊D253

Splittings

Fitting, socleC2×C11×C23×C31 ⋊ C2
derived, HallC11×C23×C31 ⋊ C22
HallC23×C31 ⋊ C2×D11
HallC11×C31 ⋊ C2×D23
HallC11×C23 ⋊ C2×D31
SylowC31 ⋊ C2×D253
SylowC23 ⋊ C2×D341
SylowC11 ⋊ C2×D713

Subgroups

subgroupG/H
center, hypercenterC2D7843
commutator, cosocle, hypocenterC11×C23×C31C22
FrattiniC1G
Fitting, socleC2×C11×C23×C31C2
LCSG ▷ C11×C23×C31
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 67
transitive degreeμt(G) = 15686

A minimal faithful permutation representation — 2 generators on 67 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);(4,13)(5,12)(6,11)(7,10)(8,9)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(38,67)(39,66)(40,65)(41,64)(42,63)(43,62)(44,61)(45,60)(46,59)(47,58)(48,57)(49,56)(50,55)(51,54)(52,53)

Conjugacy classes & character table

7846 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD31372
maximal normal subgroup ofD31372
maximal quotient ofDic15686, D31372

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31372, 32);