Finite Group Databasebeta

C22×#15688852 #26182621

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#15688852

Splittings

FittingC22×C4×C8×C47 ⋊ C2
SylowC47 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC23×C4D188
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC22×C4×C8×C47C2
socleC24×C47C22⋊C4
prime radicalC23×D188C4
cosocleC42×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C22×D4⋊C8
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

1886 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, 135911);