Finite Group Databasebeta

← Prev (#13193715) Next (#13193717) →

C7×#16500 #13193716

order1792
nilpotency class2
isoclinismisoclinic class of #16249
automorphism?
homologyAbelianization (H1) = C24×C7 · Schur multiplier (H2) = C26×C4

Aliases

direct productC7×#16500

Subgroups

subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

2698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 896

A minimal faithful permutation representation — 4 generators on 27 points:

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

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 9488);