Finite Group Databasebeta

C2×#20245359 #26370209

order12032
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20245359

Splittings

SylowC47 ⋊ C2×#2194

Subgroups

subgroupG/H
centerC22#15689257
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
Fitting, prime radicalC2×C47×#576C2
socleC22×C47#447
hypercenterC2×#576D47
hypocenterC47C2×#2194
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#576

1130 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1058 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323499);