Finite Group Databasebeta

← Prev (#24922309) Next (#24922311) →

C23×D231 #24922310

order10626
isoclinismisoclinic class of D231
automorphism?
homologyAbelianization (H1) = C2×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×D231
unambiguous semidirect productC3⋊(C23×D77)
unambiguous semidirect productC7⋊(C23×D33)
unambiguous semidirect productC11⋊(C23×D21)

Splittings

Fitting, socle, HallC3×C7×C11×C23 ⋊ C2
derived, HallC3×C7×C11 ⋊ C2×C23
HallC7×C11×C23 ⋊ D3
HallC3×C11×C23 ⋊ D7
HallC3×C7×C23 ⋊ D11
HallC11×C23 ⋊ D21
HallC7×C23 ⋊ D33
HallC7×C11 ⋊ D3×C23
HallC3×C23 ⋊ D77
HallC3×C11 ⋊ D7×C23
HallC3×C7 ⋊ D11×C23
SylowC11 ⋊ C23×D21
SylowC7 ⋊ C23×D33
SylowC3 ⋊ C23×D77

Subgroups

subgroupG/H
center, hypercenterC23D231
commutator, cosocle, hypocenterC3×C7×C11C2×C23
FrattiniC1G
Fitting, socleC3×C7×C11×C23C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2691 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23×D231, D11×C23×D21, D253⋊D21, …
maximal normal subgroup ofD23×D231, D11×C23×D21, D253⋊D21, …
maximal quotient ofC23×Dic231, C2×C23×D231, C23×D693, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 18);