Finite Group Databasebeta

D47×#1370 #26127844

order12032
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productD47×#1370

Splittings

FittingC47×#1370 ⋊ C2
SylowC47 ⋊ C2×#1370

Subgroups

subgroupG/H
centerC2×C8D4×D47
commutatorC4×C47C22×C16
FrattiniC4×C8C22×D47
FittingC47×#1370C2
socleC22×C47C2×C4⋊C8
prime radicalC22×D47C4⋊C8
cosocleC4×C8×C47C23
hypercenter#1370D47
hypocenterC47C2×#1370
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ #1370

286 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 81134);