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Dic3×ΓL(1,𝔽8)×C137 #46828604

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

Aliases

direct productDic3×ΓL(1,𝔽8)×C137
unambiguous semidirect productC3⋊(C4×ΓL(1,𝔽8)×C137)
unambiguous semidirect product(C7×Dic3)⋊(C3×C137)
unambiguous semidirect product(C7×Dic3×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×C137D3×ΓL(1,𝔽8)
commutator, hypocenterC3×C7C3×C4×C137
FrattiniC2D3×ΓL(1,𝔽8)×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

4110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34524, 47);