Finite Group Databasebeta

C2×#20244465 #26243320

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20244465

Splittings

FittingC22×#124×C47 ⋊ C2
SylowC47 ⋊ C2×#2012

Subgroups

subgroupG/H
centerC24C2×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#124×C47C2
socleC24×C47C2×D4
prime radicalC23×#10625334C2
hypercenterC22×#124D47
hypocenterC47C2×#2012
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#124

2382 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 196610);