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C2×C13×C3⋊D237 #49149663

order36972
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C13×C3⋊D237
unambiguous semidirect product(C2×C3)⋊(C13×D237)

Splittings

Fitting, socleC2×C32×C13×C79 ⋊ C2
derived, HallC32×C79 ⋊ C22×C13
HallC32×C13×C79 ⋊ C22
HallC13×C79 ⋊ C2×C3⋊D3
HallC32×C13 ⋊ C2×D79
SylowC79 ⋊ C2×C13×C3⋊D3
SylowC32 ⋊ C2×C13×D79

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊D237
commutator, cosocle, hypocenterC32×C79C22×C13
FrattiniC1G
Fitting, socleC2×C32×C13×C79C2
LCSG ▷ C32×C79
UCSC1 ◁ C2×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 100
transitive degreeμt(G) = 18486

A minimal faithful permutation representation — 3 generators on 100 points:

(4,5)(7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21)(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);(1,2)(6,7,8)(22,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24);(3,4,5)

Conjugacy classes & character table

9282 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 311);