Finite Group Databasebeta

C8×#13094031 #26181866

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×#13094031

Splittings

SylowC47 ⋊ C8×#131

Subgroups

subgroupG/H
centerC4×C8C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC42C23×D47
FittingC8×#41×C47C2
socleC22×C47C22×C42
prime radicalC2×#41×C47C2×C4
cosocleC42×C47C24
hypercenterC8×#41D47
hypocenterC47C8×#131
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C8 ◁ C8×#41

922 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, 135156);