Finite Group Databasebeta

C22×#15688925 #26369151

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

Aliases

direct productC22×#15688925

Splittings

FittingC23×C16×C47 ⋊ C2
SylowC47 ⋊ C22×#357

Subgroups

subgroupG/H
centerC24D376
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC23×C16×C47C2
socleC24×C47D8
prime radicalC23×D376C2
cosocleC2×C8×C47C24
hypercenterC23×C16D47
hypocenterC47C22×#357
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8 ◁ C23×C16

1470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322441);