Finite Group Databasebeta

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C23×#11724786 #20296096

order6976
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11724786

Splittings

derived, SylowC109 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC24#89137
commutator, hypocenterC109C23×C8
FrattiniC2C23×#89137
Fitting, socleC24×C109C4
LCSG ▷ C109
UCSC1 ◁ C24

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

496 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#20295892, #28378698, C22⋊C4×#11724786, …
maximal normal subgroup ofC2×#20295892, #28378698, C22⋊C4×#11724786, …
maximal quotient ofC22×C4×#11724786, C22×C22⋊#11724786, C22×C4⋊#11724786, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6976, 1619);