Finite Group DatabasebetaFinite Group Databasebeta| order | 4459 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C13 · Schur multiplier (H2) = C72 |
| direct product | C13×H(3,𝔽7) |
| unambiguous semidirect product | C72⋊(C7×C13) |
| unambiguous semidirect product | (C72×C13)⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C7×C13 | C72 |
| commutator, Frattini, cosocle | C7 | C72×C13 |
| LCS | G ▷ C7 ▷ C1 | |
| UCS | C1 ◁ C7×C13 ◁ G | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 637 |
A minimal faithful permutation representation — 2 generators on 62 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,21,28,39,48)(16,19,23,30,41,50,57)(18,24,34,46,55,62,56)(20,26,33,43,52,49,58)(22,31,44,54,61,47,25)(27,37,32,45,40,51,59)(29,42,53,60,38,36,35);(15,18,25,36,37,26,19)(17,22,32,23,24,35,33)(21,29,30,31,43,34,45)(28,40,46,52,44,41,42)(39,49,53,55,50,51,54)(48,57,58,59,60,61,62)715 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4459, 3);