Finite Group Databasebeta

C2×#20245079 #26369116

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

Aliases

direct productC2×#20245079

Splittings

FittingC2×C47×#413 ⋊ C2
SylowC47 ⋊ C2×#2134

Subgroups

subgroupG/H
centerC22C2×#13093938
commutatorC2×C4×C47C23×C4
FrattiniC2×Q8C23×D47
FittingC2×C47×#413C2
socleC22×C47C2×#99
prime radicalC2×#15689687C2
cosocleC2×Q8×C47C24
hypercenterC2×#413D47
hypocenterC47C2×#2134
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#413

1390 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1058 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322406);