Finite Group Databasebeta

C2×#20243742 #26217617

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20243742

Splittings

FittingC2×C47×#336 ⋊ C2
SylowC47 ⋊ C2×#1880

Subgroups

subgroupG/H
centerC24C2×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#336C2
socleC24×C47C2×D4
prime radicalC23×D188C22
cosocleC22×C4×C47C24
hypercenterC2×#336D47
hypocenterC47C2×#1880
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

2038 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 170907);