Finite Group Databasebeta

← Prev (#24922319) Next (#24922321) →

ΓL(1,𝔽8)×D11×C23 #24922320

order10626
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D11×C23
unambiguous semidirect productC11⋊(C2×ΓL(1,𝔽8)×C23)
unambiguous semidirect product(C7×D11)⋊(C3×C23)
unambiguous semidirect product(C7×D11×C23)⋊C3

Splittings

Fitting, socle, HallC7×C11×C23 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C23
HallC11×ΓL(1,𝔽8)×C23 ⋊ C2
HallC7×D11×C23 ⋊ C3
HallC11×C23 ⋊ C2×ΓL(1,𝔽8)
HallC11×ΓL(1,𝔽8) ⋊ C2×C23
HallC7×C23 ⋊ C3×D11
HallC7×D11 ⋊ C3×C23
SylowC11 ⋊ C2×ΓL(1,𝔽8)×C23
SylowC7 ⋊ C3×D11×C23

Subgroups

subgroupG/H
center, hypercenterC23ΓL(1,𝔽8)×D11
commutator, cosocle, hypocenterC7×C11C2×C3×C23
FrattiniC1G
Fitting, socleC7×C11×C23C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

805 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×C23×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D23, ΓL(1,𝔽8)×D11×D23, …
maximal normal subgroup ofD11×C23×AGL(1,𝔽7), D11×ΓL(1,𝔽8)⋊D23, ΓL(1,𝔽8)×D11×D23, …
maximal quotient ofΓL(1,𝔽8)×C23×Dic11, C2×ΓL(1,𝔽8)×D11×C23, D11×C23×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 28);