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C22×#15667734 #26015090

order11296
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC22×#15667734

Splittings

Fitting, socleC22×C353 ⋊ C8
derived, SylowC353 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC22#15667734
commutator, hypocenterC353C22×C8
FrattiniC1G
Fitting, socleC22×C353C8
prime radicalC22×D353C4
cosocle#13083443C23
LCSG ▷ C353
UCSC1 ◁ C22

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#15667734)⋊C4, C2×C4×#15667734, C2×C22⋊#15667734, …
maximal normal subgroup of(C2×#15667734)⋊C4, C2×C4×#15667734, C2×C22⋊#15667734, …
maximal quotient ofC2×C4×#15667734, C2×C22⋊#15667734, C2×C4⋊#15667734, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11296, 244);