Finite Group Databasebeta

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C23×#11924753 #23750695

order9536
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11924753

Splittings

derived, SylowC149 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC24#10597010
commutator, hypocenterC149C23×C8
FrattiniC2C23×#10597010
Fitting, socle, prime radicalC24×C149C4
cosocleDic149C24
LCSG ▷ C149
UCSC1 ◁ C24

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

656 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#23750491, #34060357, C22⋊C4×#11924753, …
maximal normal subgroup ofC2×#23750491, #34060357, C22⋊C4×#11924753, …
maximal quotient ofC22×C4×#11924753, C22×C22⋊#11924753, C22×C4⋊#11924753, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 1619);