Finite Group Databasebeta

D47×#2138 #26369156

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD47×#2138

Splittings

FittingC47×#2138 ⋊ C2
SylowC47 ⋊ C2×#2138

Subgroups

subgroupG/H
centerC2×C4D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×#2138C2
socleC22×C47C22×D8
prime radicalC2×#135×D47C2
cosocleC2×C8×C47C24
hypercenter#2138D47
hypocenterC47C2×#2138
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #2138

1190 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, 322446);