Finite Group Databasebeta

D47×#1527 #26184177

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD47×#1527

Splittings

FittingC47×#1527 ⋊ C2
SylowC47 ⋊ C2×#1527

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1527C2
socleC22×C47C22×C22⋊C4
prime radicalC22×D4×D47C4
cosocleC42×C47C24
hypercenter#1527D47
hypocenterC47C2×#1527
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1527

1394 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

800 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 137467);