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C22×D181⋊C8 #26042350

order11584
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D181⋊C8
unambiguous semidirect productD181⋊(C22×C8)

Splittings

derived, SylowC181 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#10624382
commutator, hypocenterC181C23×C8
FrattiniC2C23×#10624382
FittingC22×C4×C181C4
socleC23×C181C2×C4
prime radicalC23×D181C4
cosocleDic181C24
LCSG ▷ C181
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

784 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#10624382)⋊C8, #37549382, #37549388, …
maximal normal subgroup ofC2×(C2×#10624382)⋊C8, #37549382, #37549388, …
maximal quotient ofC22×C4×#13089685, C2×C4×D181⋊C8, C2×D181⋊(C22⋊C8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 1620);