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C22×C4×#10624382 #26042339

order11584
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C4×#10624382
unambiguous semidirect productD181⋊(C2×C42)

Splittings

FittingC22×C4×C181 ⋊ C4
derived, SylowC181 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4#10624382
commutator, hypocenterC181C22×C42
FrattiniC2C23×#10624382
FittingC22×C4×C181C4
socleC23×C181C2×C4
prime radicalC23×D181C22
cosocleC2×D181C24
LCSG ▷ C181
UCSC1 ◁ C22×C4

498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

784 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#95×#10624382, C4×(C2×#10624382)⋊C4, #37548896, …
maximal normal subgroup of#95×#10624382, C4×(C2×#10624382)⋊C4, #37548896, …
maximal quotient ofC2×C42×#10624382, C22×(C2×#10624382)⋊C4, C2×#26042215, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 1609);