Finite Group Databasebeta

C22×C3×#1136 #13061123

order1344
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×C3×#1136

Splittings

HallC3×C7 ⋊ C22×M16
SylowC7 ⋊ C22×C3×M16

Subgroups

subgroupG/H
centerC22×C3×C4C2×D7
commutatorC2×C7C23×C3×C4
FrattiniC4C23×C3×D7
FittingC23×C3×C4×C7C2
socleC23×C3×C7C2×C4
prime radicalC24×C3×C7C4
cosocleC4×C7C24×C3
hypercenterC23×C3×C4D7
hypocenterC7C22×C3×M16
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C3×C4 ◁ C23×C3×C4

596 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10412);