Finite Group Databasebeta

C2×#20241253 #26106118

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241253

Splittings

SylowC47 ⋊ C2×#1288

Subgroups

subgroupG/H
centerC23C47⋊#95
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC2×C4×M16×C47C2
socleC23×C47#95
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×C4×M16D47
hypocenterC47C2×#1288
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×M16

678 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, 59408);