Finite Group Databasebeta

C2×#20243332 #26215522

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20243332

Splittings

SylowC47 ⋊ C2×#1789

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC23×#41×C47C2
socleC23×C47C2×C22⋊C4
cosocleC22×C4×C47C24
hypercenterC23×#41D47
hypocenterC47C2×#1789
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×#41

4102 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168812);