Finite Group Databasebeta

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C2×C3×C7×C23⋊C11 #24922294

order10626
isoclinismisoclinic class of C23⋊C11
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C7×C23⋊C11
unambiguous semidirect product(C2×C23)⋊(C3×C7×C11)
unambiguous semidirect product(C2×C3×C23)⋊(C7×C11)
unambiguous semidirect product(C2×C3×C7×C23)⋊C11

Splittings

Fitting, socle, HallC2×C3×C7×C23 ⋊ C11
derived, SylowC23 ⋊ C2×C3×C7×C11
HallC3×C7×C23 ⋊ C2×C11
HallC2×C7×C23 ⋊ C3×C11
HallC7×C23 ⋊ C2×C3×C11
HallC2×C3×C23 ⋊ C7×C11
HallC3×C23 ⋊ C2×C7×C11
HallC2×C23 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C23⋊C11
commutator, cosocle, hypocenterC23C2×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C3×C7×C23C11
LCSG ▷ C23
UCSC1 ◁ C2×C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

546 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×C7×C23⋊C11, C3×C7×Dic23⋊C11, C3×Dic7×C23⋊C11, …
maximal normal subgroup ofC3×C4×C7×C23⋊C11, C3×C7×Dic23⋊C11, C3×Dic7×C23⋊C11, …
maximal quotient ofC3×C4×C7×C23⋊C11, C22×C3×C7×C23⋊C11, C2×C7×C9×C23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 2);