Finite Group Databasebeta

C8×#13093942 #26106842

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC8×#13093942

Splittings

SylowC47 ⋊ C8×#101

Subgroups

subgroupG/H
centerC2×C8(C2×D47)⋊C4
commutatorC22×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC8×M16×C47C2
socleC22×C47C4×C22⋊C4
prime radicalC23×C47C2×C42
cosocleC2×C42×C47C23
hypercenterC8×M16D47
hypocenterC47C8×#101
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C8×M16

454 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60132);