Finite Group Databasebeta

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C2×#72220578 #72341352

order3072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#72220578

Splittings

FittingC2×#14694 ⋊ D3

Subgroups

subgroupG/H
centerC23C2×#1020⋊C2
commutatorC2×C22⋊A4C23×C4
FrattiniC24C23×S4
FittingC2×#14694D3
socleC25C22×S4
prime radicalC23×#1020⋊C2C2
cosocleC22×C22⋊A4C24
hypercenterC22×C4#1020⋊C2
hypocenterC22⋊A4C22×C22⋊C4
LCSG ▷ C2×C22⋊A4 ▷ C22⋊A4
UCSC1 ◁ C23 ◁ C22×C4

At least 6004 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72341433, C2×#72222918
maximal normal subgroup of#72341433, C2×#72222918
maximal quotient of#72343876

GAP

Past the SmallGroups library coverage — no SmallGroups id.