Finite Group Databasebeta

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C2×#11864777 #72214011

order2304
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#11864777

Splittings

FittingC2×C32×#127 ⋊ C22
SylowC32 ⋊ C22×#453

Subgroups

subgroupG/H
centerC22#10595278
commutator, cosocleC2×C32×C4C25
FrattiniC2×C4C23×D32
FittingC2×C32×#127C22
socleC22×C32C2×#120
hypercenterC2×#127D32
hypocenterC32C22×#453
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

12840 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72219759, D7×#11864777, #72252285, …
maximal normal subgroup of#72215117, #72219759, #72252285, …
maximal quotient of#72219801, D3×#11864777, D7×#11864777, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.