Finite Group Databasebeta

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C7×#62832 #13240048

order1792
nilpotency class2
isoclinismisoclinic class of #62817
automorphism?
homologyAbelianization (H1) = C26×C7 · Schur multiplier (H2) = C213

Aliases

direct productC7×#62832

Subgroups

subgroupG/H
center, socleC22×C7C26
commutator, Frattini, cosocleC22C26×C7
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ G

8650 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 224

A minimal faithful permutation representation — 6 generators on 23 points:

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

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD7×#62832, #72260047
maximal subgroup ofD7×#62832, #72260047, C7×#347047
maximal normal subgroup ofD7×#62832, #72260047, C7×#347047

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 55820);