Finite Group Databasebeta

C2×#20245489 #26370722

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

Aliases

direct productC2×#20245489

Splittings

FittingC2×C47×#466 ⋊ C2
SylowC47 ⋊ C2×#2218

Subgroups

subgroupG/H
centerC23C2×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC2×C47×#466C2
socleC23×C47C2×D8
hypercenterC2×#466D47
hypocenterC47C2×#2218
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

786 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 324012);