Finite Group Databasebeta

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C17×ΓL(1,𝔽8)×D33 #37555645

order23562
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)×D33
unambiguous semidirect productC3⋊(C17×ΓL(1,𝔽8)×D11)
unambiguous semidirect productC11⋊(D3×C17×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D33)⋊(C3×C17)
unambiguous semidirect product(C7×C17×D33)⋊C3

Splittings

Fitting, socleC3×C7×C11×C17 ⋊ C2×C3
derivedC3×C7×C11 ⋊ C2×C3×C17
HallC3×C11×C17×ΓL(1,𝔽8) ⋊ C2
HallC7×C11×C17 ⋊ C3×D3
HallC3×C17×ΓL(1,𝔽8) ⋊ D11
HallC3×C11×ΓL(1,𝔽8) ⋊ C2×C17
HallC11×C17 ⋊ D3×ΓL(1,𝔽8)
HallC7×C17 ⋊ C3×D33
HallC7×C11 ⋊ C3×D3×C17
HallC3×ΓL(1,𝔽8) ⋊ C17×D11
SylowC11 ⋊ D3×C17×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C17×D33

Subgroups

subgroupG/H
center, hypercenterC17ΓL(1,𝔽8)×D33
commutator, cosocle, hypocenterC3×C7×C11C2×C3×C17
FrattiniC1G
Fitting, socleC3×C7×C11×C17C2×C3
LCSG ▷ C3×C7×C11
UCSC1 ◁ C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 39);