Finite Group Databasebeta

C2×#20241777 #26182633

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#20241777

Splittings

FittingC2×C47×D4⋊C8 ⋊ C2
SylowC47 ⋊ C2×#1478

Subgroups

subgroupG/H
centerC22×C4D4×D47
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC2×C47×D4⋊C8C2
socleC23×C47C2×C22⋊C4
prime radicalC22×D4×D47C4
cosocleC42×C47C24
hypercenterC2×D4⋊C8D47
hypocenterC47C2×#1478
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

1714 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 135923);