Finite Group Databasebeta

C2×#20241627 #26137934

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#20241627

Splittings

FittingC23×C22⋊C4×C47 ⋊ C2
SylowC47 ⋊ C2×#1438

Subgroups

subgroupG/H
centerC25C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC23×C22⋊C4×C47C2
socleC25×C47C23
prime radicalC24×C22⋊D47C2
cosocleC24×C47C24
hypercenterC23×C22⋊C4D47
hypocenterC47C2×#1438
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C25 ◁ C23×C22⋊C4

8190 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, 91224);