Finite Group Databasebeta

C2×#20244516 #26243513

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20244516

Splittings

FittingC22×#123×C47 ⋊ C2
SylowC47 ⋊ C2×#2022

Subgroups

subgroupG/H
centerC23#13093992
commutator, cosocleC24×C47C24
FrattiniC24C23×D47
FittingC22×#123×C47C2
socleC23×C47#120
prime radicalC2×#15689682C2
hypercenterC22×#123D47
hypocenterC47C2×#2022
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C22×#123

2394 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 196803);