Finite Group Databasebeta

D47×#1331 #26126007

order12032
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productD47×#1331

Splittings

FittingC47×#1331 ⋊ C2
SylowC47 ⋊ C2×#1331

Subgroups

subgroupG/H
centerC2×C4D8×D47
commutatorC8×C47C22×C8
FrattiniC4×C8C22×D47
FittingC47×#1331C2
socleC22×C47C2×#102
prime radicalC2×D8×D47C4
cosocleC4×C8×C47C23
hypercenter#1331D47
hypocenterC47C2×#1331
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1331

470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 79297);