Finite Group Databasebeta

C2×#20245075 #26369111

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

Aliases

direct productC2×#20245075

Splittings

FittingC22×#101×C47 ⋊ C2
SylowC47 ⋊ C2×#2133

Subgroups

subgroupG/H
centerC22C2×#13093938
commutatorC2×C4×C47C23×C4
FrattiniC2×Q8C23×D47
FittingC22×#101×C47C2
socleC22×C47C2×#99
prime radicalC22×#10625350C4
cosocleC2×Q8×C47C24
hypercenterC22×#101D47
hypocenterC47C2×#2133
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24 ◁ C23×Q8 ◁ C22×#101

1198 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, 322401);