Finite Group Databasebeta

C22×C3⋊D3×#127 #72214872

order2304
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214×C3×C4

Aliases

direct productC22×C3⋊D3×#127

Splittings

FittingC22×C32×#127 ⋊ C2
SylowC32 ⋊ C23×#127

Subgroups

subgroupG/H
centerC24C23×C3⋊D3
commutator, cosocleC22×C32C26
FrattiniC22C25×C3⋊D3
FittingC22×C32×#127C2
socleC24×C32C24
hypercenterC22×#127C3⋊D3
hypocenterC32C23×#127
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C24 ◁ C22×#127

72090 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72252371
maximal normal subgroup of#72252371

GAP

Past the SmallGroups library coverage — no SmallGroups id.