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C23×#11715906 #20261858

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

Aliases

direct productC23×#11715906

Splittings

Fitting, socleC23×C97 ⋊ C8
derived, SylowC97 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC23#11715906
commutator, hypocenterC97C23×C8
FrattiniC1G
Fitting, socleC23×C97C8
LCSG ▷ C97
UCSC1 ◁ C23

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#11715906)⋊C4, C22⋊C4×#11715906, #27158881, …
maximal normal subgroup ofC2×(C2×#11715906)⋊C4, C22⋊C4×#11715906, #27158881, …
maximal quotient ofC22×C4×#11715906, C22×C22⋊#11715906, C22×C4⋊#11715906, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 1672);