Finite Group Databasebeta

C8×#13093946 #26107042

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC8×#13093946

Splittings

FittingC2×C82×C47 ⋊ C2
SylowC47 ⋊ C8×#102

Subgroups

subgroupG/H
centerC22×C8D188
commutatorC4×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC2×C82×C47C2
socleC23×C47C4×D4
prime radicalC22×D188C2×C4
cosocleC2×C42×C47C23
hypercenterC2×C82D47
hypocenterC47C8×#102
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C82

606 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60332);