Finite Group Databasebeta

← Prev (#24922295) Next (#24922297) →

C2×ΓL(1,𝔽8)×C23⋊C11 #24922296

order10626
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×ΓL(1,𝔽8)×C23⋊C11
unambiguous semidirect product(C2×C7)⋊(C3×C23⋊C11)
unambiguous semidirect product(C2×C23)⋊(C11×ΓL(1,𝔽8))
unambiguous semidirect product(C2×ΓL(1,𝔽8)×C23)⋊C11
unambiguous semidirect product(C2×C7×C23⋊C11)⋊C3

Splittings

Fitting, socle, HallC2×C7×C23 ⋊ C3×C11
derived, HallC7×C23 ⋊ C2×C3×C11
HallC2×C7×C23⋊C11 ⋊ C3
HallC7×C23⋊C11 ⋊ C2×C3
HallC2×ΓL(1,𝔽8)×C23 ⋊ C11
HallΓL(1,𝔽8)×C23 ⋊ C2×C11
HallC2×C23 ⋊ C11×ΓL(1,𝔽8)
SylowC23 ⋊ C2×C11×ΓL(1,𝔽8)
HallC2×C7 ⋊ C3×C23⋊C11
SylowC7 ⋊ C2×C3×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×C23⋊C11
commutator, cosocle, hypocenterC7×C23C2×C3×C11
FrattiniC1G
Fitting, socleC2×C7×C23C3×C11
LCSG ▷ C7×C23
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×ΓL(1,𝔽8)×C23⋊C11, ΓL(1,𝔽8)×Dic23⋊C11, ΓL(1,𝔽8)⋊C4×C23⋊C11, …
maximal normal subgroup ofC4×ΓL(1,𝔽8)×C23⋊C11, ΓL(1,𝔽8)×Dic23⋊C11, ΓL(1,𝔽8)⋊C4×C23⋊C11, …
maximal quotient ofC4×ΓL(1,𝔽8)×C23⋊C11, C22×ΓL(1,𝔽8)×C23⋊C11, C2×C7⋊C9×C23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 4);