Finite Group Databasebeta

C2×#20249130 #26382641

order12032
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20249130

Splittings

FittingC23×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ C2×#2618

Subgroups

subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC23×C4⋊C4×C47C2
socleC24×C47C24
prime radicalC22×#13093998C2
hypercenterC23×C4⋊C4D47
hypocenterC47C2×#2618
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4⋊C4

3718 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 335931);