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ΓL(1,𝔽8)⋊C4×C277 #37551622

order23268
automorphism?
homologyAbelianization (H1) = C3×C4×C277 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)⋊C4×C277
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C277)
unambiguous semidirect productDic7⋊(C3×C277)

Splittings

derived, SylowC7 ⋊ C3×C4×C277
HallDic7×C277 ⋊ C3
HallΓL(1,𝔽8)×C277 ⋊ C4
HallC7×C277 ⋊ C3×C4
HallDic7 ⋊ C3×C277
HallΓL(1,𝔽8) ⋊ C4×C277

Subgroups

subgroupG/H
center, hypercenterC2×C277AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C277
FrattiniC2AGL(1,𝔽7)×C277
Fitting, socleC2×C7×C277C2×C3
prime radicalC2×ΓL(1,𝔽8)×C277C2
cosocleC2×C7C2×C3×C277
LCSG ▷ C7
UCSC1 ◁ C2×C277

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7756

Conjugacy classes & character table

3878 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23268, 18);