Finite Group Databasebeta

C2×#20245032 #26369003

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20245032

Splittings

FittingC22×#99×C47 ⋊ C2
SylowC47 ⋊ C2×#2121

Subgroups

subgroupG/H
centerC22C2×#13093938
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
FittingC22×#99×C47C2
socleC22×C47C2×#99
prime radicalC2×#15689682C2
cosocleC2×D4×C47C24
hypercenterC22×#99D47
hypocenterC47C2×#2121
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C23×D4 ◁ C22×#99

1494 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, 322293);