Finite Group Databasebeta

C22×#15688888 #26213695

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC22×#15688888

Splittings

SylowC47 ⋊ C22×#341

Subgroups

subgroupG/H
centerC23×C4D188
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC24×C8×C47C2
socleC24×C47C4⋊C4
prime radicalC25×C47Q8
cosocleC22×C4×C47C24
hypercenterC24×C8D47
hypocenterC47C22×#341
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C24×C8

2238 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 166985);