Finite Group Databasebeta

C2×#20241220 #26105713

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#20241220

Splittings

SylowC47 ⋊ C2×#1276

Subgroups

subgroupG/H
centerC2×C42C22⋊D47
commutatorC4×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC2×C47×#431C2
socleC23×C47#95
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×#431D47
hypocenterC47C2×#1276
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×#431

974 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 59003);