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C7×#15166 #13192382

order1792
nilpotency class2
isoclinismisoclinic class of #14715
automorphism?
homologyAbelianization (H1) = C24×C7 · Schur multiplier (H2) = C24

Aliases

direct productC7×#15166

Subgroups

subgroupG/H
center, socle, prime radicalC24×C7C24
commutator, Frattini, cosocleC24C24×C7
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

1310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 1792

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

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

Conjugacy classes & character table

448 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 8154);