Finite Group Databasebeta

D47×#1580 #26185673

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

Aliases

direct productD47×#1580

Splittings

FittingC47×#1580 ⋊ C2
SylowC47 ⋊ C2×#1580

Subgroups

subgroupG/H
centerC2×C4C2×D4×D47
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC47×#1580C2
socleC22×C47C2×C4×D4
prime radicalC2×D8×D47C4
cosocleC42×C47C24
hypercenter#1580D47
hypocenterC47C2×#1580
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

894 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, 138963);