Finite Group Databasebeta

C22×#15688846 #26182063

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

Aliases

direct productC22×#15688846

Splittings

FittingC22×C22⋊C8×C47 ⋊ C2
SylowC47 ⋊ C22×#323

Subgroups

subgroupG/H
centerC24(C2×D47)⋊C4
commutatorC22×C47C23×C8
FrattiniC22×C4C23×D47
FittingC22×C22⋊C8×C47C2
socleC24×C47C22⋊C4
prime radicalC25×D47C4
cosocleC22×C4×C47C24
hypercenterC22×C22⋊C8D47
hypocenterC47C22×#323
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

2878 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 135353);