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C7×#4294 #11924775

order1197
isoclinismisoclinic class of C19⋊C3
automorphism?
homologyAbelianization (H1) = C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×#4294

Splittings

derived, SylowC19 ⋊ C7×C9
HallC7×C19 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC3×C7C19⋊C3
commutator, hypocenterC19C7×C9
FrattiniC3C7×C19⋊C3
Fitting, socle, prime radicalC3×C7×C19C3
cosocleC3×C19C3×C7
LCSG ▷ C19
UCSC1 ◁ C3×C7

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 1197

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,3,4,5,6,7)(9,10,12)(11,14,15)(13,17,16)(18,22,20)(19,23,21)(24,26,25)(27,28,30,29,31,33,32,34,35);(8,9,11,15,20,25,22,10,13,18,23,12,16,21,14,19,24,26,17)

Conjugacy classes & character table

189 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×#4294⋊C2, D7×#4294, #4294⋊D7, …
maximal normal subgroup ofC7×#4294⋊C2, D7×#4294, #4294⋊D7, …
maximal quotient ofC2×C7×#4294, C7×C22⋊#4294, C7×C11×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1197, 2);