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C4×ΓL(1,𝔽8)×C263 #36348304

order22092
automorphism?
homologyAbelianization (H1) = C3×C4×C263 · Schur multiplier (H2) = C1

Aliases

direct productC4×ΓL(1,𝔽8)×C263
unambiguous semidirect product(C4×C7)⋊(C3×C263)
unambiguous semidirect product(C4×C7×C263)⋊C3

Splittings

Fitting, HallC4×C7×C263 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C263
HallC7×C263 ⋊ C3×C4
HallC4×C7 ⋊ C3×C263

Subgroups

subgroupG/H
center, hypercenterC4×C263ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C263
FrattiniC2C2×ΓL(1,𝔽8)×C263
FittingC4×C7×C263C3
socleC2×C7×C263C2×C3
prime radicalC2×ΓL(1,𝔽8)×C263C2
cosocleC2×C7C2×C3×C263
LCSG ▷ C7
UCSC1 ◁ C4×C263

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7364

Conjugacy classes & character table

5260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22092, 2);