Finite Group Databasebeta

C2×C4×#13093945 #26214016

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#13093945

Splittings

SylowC47 ⋊ C2×C4×#102

Subgroups

subgroupG/H
centerC23×C4C22⋊D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC22×C4×D4×C47C2
socleC24×C47C2×D4
prime radicalC23×D4×C47C22
cosocleC22×C4×C47C24
hypercenterC22×C4×D4D47
hypocenterC47C2×C4×#102
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×D4

2158 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 167306);