Finite Group Databasebeta

C2×C7×C3⋊#95 #13056243

order1344
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C25

Aliases

direct productC2×C7×C3⋊#95
unambiguous semidirect product(C2×C3)⋊(C7×#95)

Splittings

HallC3×C7 ⋊ C2×#95
SylowC3 ⋊ C2×C7×#95

Subgroups

subgroupG/H
centerC24×C7C2×D3
commutatorC2×C3C2×C42×C7
FrattiniC23C22×D3×C7
FittingC23×C3×C4×C7C2
socle, prime radicalC24×C3×C7C22
cosocleC23×C3C23×C7
hypercenterC23×C4×C7D3
hypocenterC3C2×C7×#95
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C24×C7 ◁ C23×C4×C7

660 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1344

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, 5532);