Finite Group Databasebeta

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C8×#13093983 #26214481

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC8×#13093983

Splittings

SylowC47 ⋊ C8×#117

Subgroups

subgroupG/H
centerC2×C4×C8C2×D47
commutatorC2×C47C22×C4×C8
FrattiniC22×C4C23×D47
FittingC22×C4×C8×C47C2
socleC23×C47C23×C4
prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C8×#117
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4×C8 ◁ C22×C4×C8

1174 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, 167771);