Finite Group Databasebeta

C4×#15688978 #26137484

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#15688978

Splittings

FittingC2×C4×C22⋊C4×C47 ⋊ C2
SylowC47 ⋊ C4×#379

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC25×D47C22
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C4×#379
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

6734 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 90774);