Finite Group Databasebeta

C2×#20243927 #26218286

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

Aliases

direct productC2×#20243927

Splittings

FittingC22×#99×C47 ⋊ C2
SylowC47 ⋊ C2×#1913

Subgroups

subgroupG/H
centerC22#15688999
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC22×#99×C47C2
socleC22×C47#386
prime radicalC2×#15689682C2
cosocleC24×C47C24
hypercenterC22×#99D47
hypocenterC47C2×#1913
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

2078 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 171576);