Finite Group Databasebeta

D47×#1778 #26214377

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productD47×#1778

Splittings

FittingC47×#1778 ⋊ C2
SylowC47 ⋊ C2×#1778

Subgroups

subgroupG/H
centerC2×C4C2×D4×D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC47×#1778C2
socleC22×C47C22×C4⋊C4
prime radicalC23×D47C2×Q8
cosocleC22×C4×C47C24
hypercenter#1778D47
hypocenterC47C2×#1778
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1778

1046 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, 167667);