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C23×#13083443 #26015081

order11296
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×#13083443
unambiguous semidirect productD353⋊(C22×C4)

Splittings

Fitting, socleC23×C353 ⋊ C4
derived, SylowC353 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC23#13083443
commutator, hypocenterC353C23×C4
FrattiniC1G
Fitting, socleC23×C353C4
prime radicalC23×D353C2
cosocleD353C24
LCSG ▷ C353
UCSC1 ◁ C23

236 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#13083443)⋊C4, C22⋊C4×#13083443, #36378734, …
maximal normal subgroup ofC2×(C2×#13083443)⋊C4, C22⋊C4×#13083443, #36378734, …
maximal quotient ofC22×C4×#13083443, C22×C22⋊#13083443, C22×C4⋊#13083443, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11296, 235);