Finite Group Databasebeta

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C23×#11764049 #22578526

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

Aliases

direct productC23×#11764049

Splittings

Fitting, socleC23×C137 ⋊ C8
derived, SylowC137 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC23#11764049
commutator, hypocenterC137C23×C8
FrattiniC1G
Fitting, socleC23×C137C8
LCSG ▷ C137
UCSC1 ◁ C23

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#11764049)⋊C4, C22⋊C4×#11764049, #31797934, …
maximal normal subgroup ofC2×(C2×#11764049)⋊C4, C22⋊C4×#11764049, #31797934, …
maximal quotient ofC22×C4×#11764049, C22×C22⋊#11764049, C22×C4⋊#11764049, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8768, 1672);