Finite Group Databasebeta

C2×#20245007 #26368966

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20245007

Splittings

FittingC2×C47×#349 ⋊ C2
SylowC47 ⋊ C2×#2115

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C23×C8
FrattiniC2×C8C23×D47
FittingC2×C47×#349C2
socleC22×C47C2×C22⋊C8
prime radicalC22×#10625350C4
cosocleC2×C8×C47C24
hypercenterC2×#349D47
hypocenterC47C2×#2115
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#349

1154 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322256);