Finite Group DatabasebetaFinite Group Databasebeta| order | 28470 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#19151048 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C13×C73 | C2×C3 |
| LCS | G ▷ C5×C13×C73 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 4745 |
A minimal faithful permutation representation — 2 generators on 91 points:
(2,3)(4,5)(7,11,12,8,9,13)(10,17,16,14,15,18)(20,24,25,21,22,26)(23,32,33,27,28,42)(29,45,46,35,36,59)(30,44,40,38,34,31)(37,64,65,48,49,77)(39,62,63,51,47,56)(41,43,61,53,54,57)(50,69,75,55,60,78)(52,79,80,67,66,74)(58,83,82,71,72,70)(68,88,89,81,76,90)(73,91,86,84,85,87);(1,2,4,5,3)(6,7,10,9,13,16,15,17,18,12,11,14,8)(19,20,23,29,37,50,53,40,25,24,30,39,52,68,82,63,33,44,32,43,58,73,86,80,46,61,62,45,60,76,85,89,65,78,83,79,64,49,66,72,75,77,90,91,88,69,36,47,57,59,74,87,84,71,54,28,34,42,56,70,81,67,51,38,22,26,31,41,55,48,35,27,21)Polycyclic presentation:
2,3,5,13,73|c^a=c^4,d^a=d^12,e^a=e^72,d^b=d^3,e^b=e^64802 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28470, 48);