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C137×C3⋊(ΓL(1,𝔽8)⋊C4) #46828602

order34524
automorphism?
homologyAbelianization (H1) = C3×C4×C137 · Schur multiplier (H2) = C1

Aliases

direct productC137×C3⋊(ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productC3⋊(ΓL(1,𝔽8)⋊C4×C137)
unambiguous semidirect productΓL(1,𝔽8)⋊(Dic3×C137)
unambiguous semidirect productDic21⋊(C3×C137)
unambiguous semidirect product(Dic21×C137)⋊C3

Splittings

derivedC3×C7 ⋊ C3×C4×C137
HallC3×ΓL(1,𝔽8)×C137 ⋊ C4
HallC7×C137 ⋊ C3×Dic3
HallC3×ΓL(1,𝔽8) ⋊ C4×C137
SylowC7 ⋊ C3×Dic3×C137

Subgroups

subgroupG/H
center, hypercenterC2×C137C3⋊AGL(1,𝔽7)
commutator, hypocenterC3×C7C3×C4×C137
FrattiniC2C3⋊AGL(1,𝔽7)×C137
Fitting, socleC2×C3×C7×C137C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C137C2
cosocleC2×C3×C7C2×C3×C137
LCSG ▷ C3×C7
UCSC1 ◁ C2×C137

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11508

Conjugacy classes & character table

3288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34524, 45);