Finite Group Databasebeta

C2×#20243081 #26213632

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20243081

Splittings

SylowC47 ⋊ C2×#1728

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C22×C42
FrattiniC22×C4C23×D47
FittingC23×M16×C47C2
socleC24×C47C22×C4
prime radicalC25×C47C2×C4
cosocleC22×C4×C47C24
hypercenterC23×M16D47
hypocenterC47C2×#1728
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C23×M16

2782 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 166922);