Finite Group Databasebeta

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C7×#18814 #13196030

order1792
nilpotency class3
isoclinismisoclinic class of #18810
automorphism?
homologyAbelianization (H1) = C24×C7 · Schur multiplier (H2) = C25

Aliases

direct productC7×#18814

Subgroups

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

1262 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)(8,9)(10,14)(11,13)(12,15)(16,17)(18,24)(19,27)(20,22)(21,26)(23,28)(25,31)(29,30);(9,13)(10,11)(14,15)(19,28)(23,27)(24,31)(26,29);(16,18)(17,21)(19,29)(20,25)(22,30)(23,31)(24,27)(26,28);(8,10,12,11)(9,14,15,13)(17,22)(21,30)(23,27)(24,31)

Conjugacy classes & character table

259 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 11802);