Finite Group Databasebeta

C2×#20243188 #26213976

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

Aliases

direct productC2×#20243188

Splittings

SylowC47 ⋊ C2×#1757

Subgroups

subgroupG/H
centerC2×C8C22⋊Dic47
commutatorC22×C47C22×C42
FrattiniC22×C4C23×D47
FittingC22×#131×C47C2
socleC22×C47C4×C22⋊C4
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC22×#131D47
hypocenterC47C2×#1757
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×#131

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, 167266);