Finite Group Databasebeta

C2×#20245105 #26369166

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20245105

Splittings

FittingC22×M32×C47 ⋊ C2
SylowC47 ⋊ C2×#2140

Subgroups

subgroupG/H
centerC23C2×D376
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC22×M32×C47C2
socleC23×C47C2×D8
prime radicalC23×D376C2
cosocleC2×C8×C47C24
hypercenterC22×M32D47
hypocenterC47C2×#2140
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

1406 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322456);