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C3×ΓL(1,𝔽8)×C361 #36384453

order22743
automorphism?
homologyAbelianization (H1) = C32×C361 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×C361
unambiguous semidirect productC7⋊(C32×C361)
unambiguous semidirect product(C3×C7)⋊(C3×C361)

Splittings

FittingC3×C7×C361 ⋊ C3
derived, SylowC7 ⋊ C32×C361
HallC7×C361 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C361ΓL(1,𝔽8)
commutator, hypocenterC7C32×C361
FrattiniC19C3×C19×ΓL(1,𝔽8)
FittingC3×C7×C361C3
socleC3×C7×C19C3×C19
prime radicalC3×C19×ΓL(1,𝔽8)C19
cosocleC7×C19C32×C19
LCSG ▷ C7
UCSC1 ◁ C3×C361

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7581

Conjugacy classes & character table

5415 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22743, 12);