Finite Group Databasebeta

C2×#20245030 #26369000

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

Aliases

direct productC2×#20245030

Splittings

FittingC2×C47×#413 ⋊ C2
SylowC47 ⋊ C2×#2120

Subgroups

subgroupG/H
centerC2×C4#13093938
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
FittingC2×C47×#413C2
socleC22×C47C2×#99
prime radicalC2×#15689630C2
cosocleC2×D4×C47C24
hypercenterC2×#413D47
hypocenterC47C2×#2120
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#413

1398 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322290);