Finite Group Databasebeta

C2×#20245740 #26374482

order12032
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#20245740

Splittings

FittingC2×C4×C22⋊C4×C47 ⋊ C2
SylowC47 ⋊ C2×#2273

Subgroups

subgroupG/H
centerC24C23×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC2×C4×C22⋊C4×C47C2
socleC24×C47C24
prime radicalC25×D47C22
cosocleC23×C47C25
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C2×#2273
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

5790 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327772);