Finite Group Databasebeta

C2×#20245124 #26369220

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

Aliases

direct productC2×#20245124

Splittings

SylowC47 ⋊ C2×#2145

Subgroups

subgroupG/H
centerC2×C4#13093945
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
Fitting, prime radicalC22×#135×C47C2
socleC22×C47C2×#102
cosocleC2×C8×C47C24
hypercenterC22×#135D47
hypocenterC47C2×#2145
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×#135

1170 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322510);