Finite Group Databasebeta

C2×C4×#13093981 #26374464

order12032
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×C4×#13093981

Splittings

FittingC2×C43×C47 ⋊ C2
SylowC47 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC22×C42C2×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC2×C43×C47C2
socleC24×C47C24
prime radicalC24×D47C23
cosocleC23×C47C25
hypercenterC2×C43D47
hypocenterC47C2×C4×#117
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C42 ◁ C2×C43

4462 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327754);