Finite Group Databasebeta

C22×#15688913 #26368993

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

Aliases

direct productC22×#15688913

Splittings

SylowC47 ⋊ C22×#352

Subgroups

subgroupG/H
centerC23#13093939
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
FittingC22×#123×C47C2
socleC23×C47#99
prime radicalC23×D4×C47C22
cosocleC2×D4×C47C24
hypercenterC22×#123D47
hypocenterC47C22×#352
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24 ◁ C23×D4 ◁ C22×#123

1486 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322283);