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C3×ΓL(1,𝔽8)×Dic137 #46828601

order34524
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×Dic137
unambiguous semidirect product(C7×Dic137)⋊C32
unambiguous semidirect product(C3×C7×Dic137)⋊C3

Splittings

derived, HallC7×C137 ⋊ C32×C4
HallC3×ΓL(1,𝔽8)×C137 ⋊ C4
HallC7×Dic137 ⋊ C32
SylowC137 ⋊ C3×C4×ΓL(1,𝔽8)
SylowC7 ⋊ C32×Dic137

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×D137
commutator, hypocenterC7×C137C32×C4
FrattiniC2C3×ΓL(1,𝔽8)×D137
Fitting, socleC2×C3×C7×C137C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C137C2
cosocleC2×C7×C137C2×C32
LCSG ▷ C7×C137
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11508

Conjugacy classes & character table

2100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34524, 44);