Finite Group Databasebeta

C8×C22⋊(C47⋊C8) #26106743

order12032
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C23×C8

Aliases

direct productC8×C22⋊(C47⋊C8)

Splittings

SylowC47 ⋊ C8×C22⋊C8

Subgroups

subgroupG/H
centerC2×C4×C8C2×D47
commutatorC2×C47C2×C82
FrattiniC2×C42C22×D47
FittingC22×C4×C8×C47C2
socleC23×C47C2×C42
prime radicalC24×C47C42
cosocleC2×C42×C47C23
hypercenterC22×C4×C8D47
hypocenterC47C8×C22⋊C8
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4×C8 ◁ C22×C4×C8

726 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60033);