Finite Group Databasebeta

C2×#20244102 #26219023

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20244102

Splittings

SylowC47 ⋊ C2×#1938

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#408C2
socleC23×C47C4×D4
prime radicalC22×#41×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#408D47
hypocenterC47C2×#1938
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C2×#408

1074 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, 172313);