Finite Group Databasebeta

C2×#20243334 #26215536

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20243334

Splittings

FittingC22×#99×C47 ⋊ C2
SylowC47 ⋊ C2×#1790

Subgroups

subgroupG/H
centerC23#13093994
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC22×#99×C47C2
socleC23×C47#120
prime radicalC22×#13094069C2
cosocleC24×C47C24
hypercenterC22×#99D47
hypocenterC47C2×#1790
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

4402 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168826);