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C23×#11757210 #21440731

order7712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11757210
unambiguous semidirect productD241⋊(C22×C4)

Splittings

Fitting, socleC23×C241 ⋊ C4
derived, SylowC241 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC23#11757210
commutator, hypocenterC241C23×C4
FrattiniC1G
Fitting, socleC23×C241C4
LCSG ▷ C241
UCSC1 ◁ C23

236 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

512 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#11757210)⋊C4, C22⋊C4×#11757210, #29508664, …
maximal normal subgroup ofC2×(C2×#11757210)⋊C4, C22⋊C4×#11757210, #29508664, …
maximal quotient ofC22×C4×#11757210, C22×C22⋊#11757210, C22×C4⋊#11757210, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7712, 235);