Finite Group Databasebeta

C2×#20241233 #26105906

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

Aliases

direct productC2×#20241233

Splittings

SylowC47 ⋊ C2×#1281

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic47
commutatorC22×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC22×#97×C47C2
socleC23×C47#95
prime radicalC24×C47C42
cosocleC2×C42×C47C23
hypercenterC22×#97D47
hypocenterC47C2×#1281
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×#97

678 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, 59196);