Finite Group Databasebeta

C8×#13093980 #26214478

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

Aliases

direct productC8×#13093980

Splittings

SylowC47 ⋊ C8×#117

Subgroups

subgroupG/H
centerC22×C8C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC8×C22⋊C4×C47C2
socleC23×C47C23×C4
prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC8×C22⋊C4D47
hypocenterC47C8×#117
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C8×C22⋊C4

1174 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167768);