Finite Group Databasebeta

C2×#20245037 #26369009

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

Aliases

direct productC2×#20245037

Splittings

FittingC2×C47×#410 ⋊ C2
SylowC47 ⋊ C2×#2122

Subgroups

subgroupG/H
centerC22C2×#13093938
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
FittingC2×C47×#410C2
socleC22×C47C2×#99
prime radicalC2×#15689687C2
cosocleC2×D4×C47C24
hypercenterC2×#410D47
hypocenterC47C2×#2122
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#410

1406 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1058 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322299);