Finite Group Databasebeta

C2×#99×Dic47 #26213926

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#99×Dic47

Splittings

SylowC47 ⋊ C2×C4×#99

Subgroups

subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC22×#99×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D4×C47C22
cosocleC24×C47C24
hypercenterC22×#99D47
hypocenterC47C2×C4×#99
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

2242 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, 167216);