Finite Group Databasebeta

C2×C42×D188 #26374471

order12032
isoclinismisoclinic class of Dic94
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C42×D188

Splittings

FittingC2×C43×C47 ⋊ C2
SylowC47 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC22×C42C2×D47
commutatorC2×C47C23×C42
FrattiniC23C24×D47
FittingC2×C43×C47C2
socleC24×C47C24
prime radicalC23×D188C22
cosocleC23×C47C25
hypercenterC2×C43D47
hypocenterC47C2×C42×D4
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C42 ◁ C2×C43

5694 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, 327761);