Finite Group Databasebeta

C8×#13094007 #26223237

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#13094007

Splittings

FittingC22×C4×C8×C47 ⋊ C2
SylowC47 ⋊ C8×#123

Subgroups

subgroupG/H
centerC22×C8C22×D47
commutatorC22×C47C23×C8
FrattiniC22×C4C23×D47
FittingC22×C4×C8×C47C2
socleC23×C47C23×C4
prime radicalC22×C22⋊D47C2×C4
cosocleC22×C4×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C8×#123
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C22×C4×C8

1034 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 176527);