Finite Group Databasebeta

D47×#1276 #26105712

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productD47×#1276

Splittings

FittingC47×#1276 ⋊ C2
SylowC47 ⋊ C2×#1276

Subgroups

subgroupG/H
centerC42D4×D47
commutatorC4×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC47×#1276C2
socleC22×C47C2×#95
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1276D47
hypocenterC47C2×#1276
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C42 ◁ C2×C42 ◁ #1276

974 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, 59002);