Finite Group Databasebeta

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C23×#11764047 #22578473

order8768
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11764047

Splittings

derived, SylowC137 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC24#10587739
commutator, hypocenterC137C23×C8
FrattiniC2C23×#10587739
Fitting, socleC24×C137C4
LCSG ▷ C137
UCSC1 ◁ C24

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#22578269, #31796455, C22⋊C4×#11764047, …
maximal normal subgroup ofC2×#22578269, #31796455, C22⋊C4×#11764047, …
maximal quotient ofC22×C4×#11764047, C22×C22⋊#11764047, C22×C4⋊#11764047, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 1619);