Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C59 · Schur multiplier (H2) = C28 |
| direct product | C59×#62178 |
| 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 ◁ C59×#529 ◁ G | |
1646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2,5,8)(3,9,10,6)(4,12,13,7)(11,14,16,15)(17,18,22,25)(19,23,28,37)(20,30,32,40)(21,33,35,26)(24,34,39,31)(27,41,42,48)(29,45,44,38)(36,46,47,43)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3)(2,6)(4,11)(5,10)(7,14)(8,9)(12,15)(13,16)(17,19)(18,23)(20,27)(21,29)(22,28)(24,36)(25,37)(26,38)(30,41)(31,43)(32,42)(33,45)(34,46)(35,44)(39,47)(40,48);(17,20,22,32)(18,24,25,39)(19,27,28,42)(21,34,35,31)(23,36,37,47)(26,40,33,30)(29,46,44,43)(38,48,45,41);(3,10)(6,9)(11,16)(14,15)(18,25)(23,37)(24,39)(26,33)(30,40)(36,47)(38,45)(41,48);(1,4,5,13)(2,7,8,12)(3,11,10,16)(6,14,9,15)(19,28)(23,37)(27,42)(29,44)(36,47)(38,45)(41,48)(43,46)2891 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 55166);