Finite Group Databasebeta

C2×#20241929 #26183531

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20241929

Splittings

FittingC2×C47×#380 ⋊ C2
SylowC47 ⋊ C2×#1513

Subgroups

subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#380C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#15689634C2
cosocleC22×C4×C47C24
hypercenterC2×#380D47
hypocenterC47C2×#1513
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

1510 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 136821);