Finite Group Databasebeta

C2×#20241239 #26105959

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241239

Splittings

SylowC47 ⋊ C2×#1283

Subgroups

subgroupG/H
centerC22×C4(C2×D47)⋊C4
commutatorC22×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC2×C4×M16×C47C2
socleC23×C47#95
prime radicalC24×C47C42
cosocleC2×C42×C47C23
hypercenterC2×C4×M16D47
hypocenterC47C2×#1283
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

722 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 59249);