Finite Group Databasebeta

C2×#20244985 #26368913

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20244985

Splittings

SylowC47 ⋊ C2×#2108

Subgroups

subgroupG/H
centerC22×C8C22×D47
commutatorC2×C47C22×C4×C8
FrattiniC2×C8C23×D47
FittingC2×C47×#405C2
socleC23×C47C22×C8
prime radicalC24×C47C2×C8
cosocleC2×C8×C47C24
hypercenterC2×#405D47
hypocenterC47C2×#2108
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C2×#405

854 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322203);