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C22×C4×#10621924 #26012551

order11072
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C4×#10621924
unambiguous semidirect productD173⋊(C2×C42)

Splittings

FittingC22×C4×C173 ⋊ C4
derived, SylowC173 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4#10621924
commutator, hypocenterC173C22×C42
FrattiniC2C23×#10621924
FittingC22×C4×C173C4
socleC23×C173C2×C4
prime radicalC23×D173C22
cosocleC2×D173C24
LCSG ▷ C173
UCSC1 ◁ C22×C4

498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

752 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#95×#10621924, C4×(C2×#10621924)⋊C4, #36368738, …
maximal normal subgroup of#95×#10621924, C4×(C2×#10621924)⋊C4, #36368738, …
maximal quotient ofC2×C42×#10621924, C22×(C2×#10621924)⋊C4, C2×#26012427, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11072, 1609);