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C7×#4296 #11924779

order1197
isoclinismisoclinic class of #4296
automorphism?
homologyAbelianization (H1) = C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×#4296

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7#4296
commutator, hypocenterC19C7×C9
FrattiniC1G
Fitting, socleC7×C19C9
prime radicalC7×C19⋊C3C3
cosocleC19⋊C3C3×C7
LCSG ▷ C19
UCSC1 ◁ C7

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 133

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5,6,7)(9,10,13,11,14,20,16,21,15)(12,17,24,18,25,26,19,23,22);(8,9,12,19,10,15,21,11,17,14,22,16,23,24,18,26,13,20,25)

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×AGL(1,𝔽19), #4296⋊D7, D7×#4296, …
maximal normal subgroup ofC7×AGL(1,𝔽19), #4296⋊D7, D7×#4296, …
maximal quotient ofC2×C7×#4296, C7×C22⋊#4296, C7×C11×#4296, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1197, 6);