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C2×C11×ΓL(1,𝔽8)×C23 #24922295

order10626
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C23 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC2×C7×C11×C23 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C11×C23
HallC7×C11×C23 ⋊ C2×C3
HallC2×C7×C23 ⋊ C3×C11
HallC7×C23 ⋊ C2×C3×C11
HallC2×C7×C11 ⋊ C3×C23
HallC7×C11 ⋊ C2×C3×C23
HallC2×C7 ⋊ C3×C11×C23

Subgroups

subgroupG/H
center, hypercenterC2×C11×C23ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C2×C3×C11×C23
FrattiniC1G
Fitting, socleC2×C7×C11×C23C3
LCSG ▷ C7
UCSC1 ◁ C2×C11×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2530 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C11×ΓL(1,𝔽8)×C23, C11×ΓL(1,𝔽8)×Dic23, ΓL(1,𝔽8)×C23×Dic11, …
maximal normal subgroup ofC4×C11×ΓL(1,𝔽8)×C23, C11×ΓL(1,𝔽8)×Dic23, ΓL(1,𝔽8)×C23×Dic11, …
maximal quotient ofC4×C11×ΓL(1,𝔽8)×C23, C22×C11×ΓL(1,𝔽8)×C23, C2×C11×C23×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 3);