Finite Group Databasebeta

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C2×#72342683 #72342745

order6144
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×#72342683

Splittings

FittingC2×#6372601 ⋊ D3

Subgroups

subgroupG/H
centerC2×C8C2×#1020⋊C2
commutatorC2×C22⋊A4C24×C4
FrattiniC22×C4C24×S4
FittingC2×#6372601D3
socleC24C22×C4×S4
prime radicalC2×#72220637C2
cosocleC4×C22⋊A4C25
hypercenterC22×C8#1020⋊C2
hypocenterC22⋊A4C22×#131
LCSG ▷ C2×C22⋊A4 ▷ C22⋊A4
UCSC1 ◁ C2×C8 ◁ C22×C8

At least 14535 conjugacy classes of subgroups; only the 964 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

Relationships

automorphism group ofC2×#2258

GAP

Past the SmallGroups library coverage — no SmallGroups id.