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C23×#11759967 #22551681

order8224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11759967
unambiguous semidirect productD257⋊(C22×C4)

Splittings

Fitting, socleC23×C257 ⋊ C4
derived, SylowC257 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC23#11759967
commutator, hypocenterC257C23×C4
FrattiniC1G
Fitting, socleC23×C257C4
LCSG ▷ C257
UCSC1 ◁ C23

236 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#11759967)⋊C4, C22⋊C4×#11759967, #30657684, …
maximal normal subgroup ofC2×(C2×#11759967)⋊C4, C22⋊C4×#11759967, #30657684, …
maximal quotient ofC22×C4×#11759967, C22×C22⋊#11759967, C22×C4⋊#11759967, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8224, 235);