Finite Group Databasebeta

C2×#20241715 #26182115

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

Aliases

direct productC2×#20241715

Splittings

SylowC47 ⋊ C2×#1462

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC23×C22⋊C4×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC26×C47C4
cosocleC22×C4×C47C24
hypercenterC23×C22⋊C4D47
hypocenterC47C2×#1462
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×C22⋊C4

2790 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, 135405);