Finite Group Databasebeta

C4×#15688857 #26107152

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#15688857

Splittings

SylowC47 ⋊ C4×#327

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC4×#121×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#121×C47C22
cosocleC23×C4×C47C23
hypercenterC4×#121D47
hypocenterC47C4×#327
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#121

816 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60442);