Finite Group Databasebeta

C22×C7×#208 #13061497

order1344
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25

Aliases

direct productC22×C7×#208

Splittings

HallC3×C7 ⋊ C22×M16
SylowC3 ⋊ C22×C7×M16

Subgroups

subgroupG/H
centerC22×C4×C7C2×D3
commutatorC2×C3C23×C4×C7
FrattiniC4C23×D3×C7
FittingC23×C3×C4×C7C2
socleC23×C3×C7C2×C4
prime radicalC24×C3×C7C4
cosocleC3×C4C24×C7
hypercenterC23×C4×C7D3
hypocenterC3C22×C7×M16
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4×C7 ◁ C23×C4×C7

596 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10786);