Finite Group Databasebeta

C2×#20243773 #26217827

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#20243773

Splittings

FittingC2×C47×#419 ⋊ C2
SylowC47 ⋊ C2×#1885

Subgroups

subgroupG/H
centerC23#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#419C2
socleC23×C47#120
prime radicalC23×D188C22
cosocleC22×C4×C47C24
hypercenterC2×#419D47
hypocenterC47C2×#1885
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

1966 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 171117);