Finite Group Databasebeta

C2×#20243189 #26213977

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20243189

Splittings

FittingC2×C47×#405 ⋊ C2
SylowC47 ⋊ C2×#1757

Subgroups

subgroupG/H
centerC2×C8(C2×D47)⋊C4
commutatorC22×C47C22×C42
FrattiniC22×C4C23×D47
FittingC2×C47×#405C2
socleC22×C47C4×C22⋊C4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×#405D47
hypocenterC47C2×#1757
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C2×#405

1474 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167267);