Finite Group Databasebeta

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C2×#11797801 #72255342

order2304
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3

Aliases

direct productC2×#11797801

Splittings

FittingC2×C32×#357 ⋊ C2
SylowC32 ⋊ C2×#2177

Subgroups

subgroupG/H
centerC23D8×C3⋊D3
commutatorC32×C8C23×C4
FrattiniC2×C8C23×C3⋊D3
FittingC2×C32×#357C2
socleC23×C32C2×D8
prime radicalC22×#63653C2
cosocleC2×C32×C8C24
hypercenterC2×#357C3⋊D3
hypocenterC32C2×#2177
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

2394 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3⋊D3×#2177
maximal normal subgroup ofC2×C3⋊D3×#2177

GAP

Past the SmallGroups library coverage — no SmallGroups id.