Finite Group Databasebeta

C8×#13093981 #26214482

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×#13093981

Splittings

FittingC42×C8×C47 ⋊ C2
SylowC47 ⋊ C8×#117

Subgroups

subgroupG/H
centerC2×C4×C8C2×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC42×C8×C47C2
socleC23×C47C23×C4
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenterC42×C8D47
hypocenterC47C8×#117
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4×C8 ◁ C42×C8

1174 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167772);