Finite Group Databasebeta

C2×#20244264 #26220114

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

Aliases

direct productC2×#20244264

Splittings

FittingC22×#97×C47 ⋊ C2
SylowC47 ⋊ C2×#1972

Subgroups

subgroupG/H
centerC24C2×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#97×C47C2
socleC24×C47C2×D4
prime radicalC23×D376C2
cosocleC22×C4×C47C24
hypercenterC22×#97D47
hypocenterC47C2×#1972
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#97

2006 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 173404);