Finite Group Databasebeta

D47×#2115 #26368965

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productD47×#2115

Splittings

FittingC47×#2115 ⋊ C2
SylowC47 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC8C22⋊C4×D47
commutatorC22×C47C23×C8
FrattiniC2×C8C23×D47
FittingC47×#2115C2
socleC2×C47C22×C22⋊C8
prime radicalC2×#41×D47C4
cosocleC2×C8×C47C24
hypercenter#2115D47
hypocenterC47C2×#2115
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2115

1154 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, 322255);