Finite Group Databasebeta

C8×#13093952 #26106986

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

Aliases

direct productC8×#13093952

Splittings

FittingC42×C8×C47 ⋊ C2
SylowC47 ⋊ C8×#104

Subgroups

subgroupG/H
centerC4×C8D188
commutatorC4×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC42×C8×C47C2
socleC22×C47C4×C22⋊C4
prime radicalC2×#10625350C2×C4
cosocleC2×C42×C47C23
hypercenterC42×C8D47
hypocenterC47C8×#104
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C8 ◁ C2×C4×C8 ◁ C42×C8

554 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, 60276);