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C23×#11764308 #22579969

order8864
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11764308
unambiguous semidirect productD277⋊(C22×C4)

Splittings

Fitting, socleC23×C277 ⋊ C4
derived, SylowC277 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC23#11764308
commutator, hypocenterC277C23×C4
FrattiniC1G
Fitting, socleC23×C277C4
LCSG ▷ C277
UCSC1 ◁ C23

236 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

584 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#11764308)⋊C4, C22⋊C4×#11764308, #31800949, …
maximal normal subgroup ofC2×(C2×#11764308)⋊C4, C22⋊C4×#11764308, #31800949, …
maximal quotient ofC22×C4×#11764308, C22×C22⋊#11764308, C22×C4⋊#11764308, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8864, 235);