Finite Group Databasebeta

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C7×#18618 #13195834

order1792
nilpotency class3
isoclinismisoclinic class of #18618
automorphism?
homologyAbelianization (H1) = C24×C7 · Schur multiplier (H2) = C25

Aliases

direct productC7×#18618

Subgroups

subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC42C24×C7
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

1084 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 448

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

322 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 11606);