Finite Group Databasebeta

← Prev (#20301076) Next (#20301078) →

C23×#11745021 #20301077

order7328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11745021
unambiguous semidirect productD229⋊(C22×C4)

Splittings

Fitting, socleC23×C229 ⋊ C4
derived, SylowC229 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC23#11745021
commutator, hypocenterC229C23×C4
FrattiniC1G
Fitting, socleC23×C229C4
LCSG ▷ C229
UCSC1 ◁ C23

236 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

488 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#11745021)⋊C4, C22⋊C4×#11745021, #28412428, …
maximal normal subgroup ofC2×(C2×#11745021)⋊C4, C22⋊C4×#11745021, #28412428, …
maximal quotient ofC22×C4×#11745021, C22×C22⋊#11745021, C22×C4⋊#11745021, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7328, 235);