Finite Group Databasebeta

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C23×#11715895 #20261492

order6208
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11715895

Splittings

derived, SylowC97 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC23×C4D97
commutator, hypocenterC97C23×C8
FrattiniC4C23×D97
FittingC23×C4×C97C2
socleC24×C97C4
LCSG ▷ C97
UCSC1 ◁ C23×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×#20260489, C2×#20260490, #27141433, …
maximal normal subgroup ofC2×#20260489, C2×#20260490, #27141433, …
maximal quotient ofC22×C4×#11715895, C22×C22⋊#11715895, C22×C4⋊#11715895, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 1306);