Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60750 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C28 |
| direct product | C59×#60961 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C59 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C42×C59 ◁ G | |
1826 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 5 generators on 91 points:
(1,2)(3,9)(4,8)(5,7)(6,10)(11,15)(12,14)(13,16)(17,18)(19,26)(20,24)(21,29)(22,25)(23,27)(28,31)(30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3)(2,6)(4,11)(5,10)(7,9)(8,13)(12,16)(14,15);(3,10)(6,9)(11,16)(13,15)(17,19)(18,23)(20,27)(21,30)(22,28)(24,31)(25,32)(26,29);(2,7)(6,9)(8,14)(13,15)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,32,26);(1,4,5,12)(2,8,7,14)(3,11,10,16)(6,13,9,15)(18,25)(23,32)(24,29)(26,31)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 53949);