Finite Group Databasebeta

M32×C47⋊C8 #26125255

order12032
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C2×C8

Aliases

direct productM32×C47⋊C8

Splittings

SylowC47 ⋊ C8×M32

Subgroups

subgroupG/H
center, FrattiniC4×C8C22×D47
commutatorC2×C47C2×C82
FittingC4×M32×C47C2
socleC22×C47C2×C4×C8
prime radicalC23×C47C4×C8
cosocleC4×C8×C47C23
hypercenterC4×M32D47
hypocenterC47C8×M32
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C8 ◁ C4×M32

354 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, 78545);