Finite Group Databasebeta

C22×#15688856 #26183355

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

Aliases

direct productC22×#15688856

Splittings

FittingC22×#95×C47 ⋊ C2
SylowC47 ⋊ C22×#327

Subgroups

subgroupG/H
centerC24(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#95×C47C2
socleC24×C47C22⋊C4
prime radicalC22×#13093998C2
cosocleC22×C4×C47C24
hypercenterC22×#95D47
hypocenterC47C22×#327
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#95

2190 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 136645);