Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#21478 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C59 | C2×#120 |
| commutator | C2×C4 | C23×C4×C59 |
| Frattini, cosocle | C22×C4 | C24×C59 |
| socle | C2×C59 | C4×#120 |
| prime radical | C59×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C59 ◁ C22×C8×C59 ◁ G | |
1282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,7,12,8,13,6,19)(3,14,17,9,18,28,23,27)(4,10,20,5,11,21,24,22)(15,16,30,32,26,29,31,25)(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)(2,9)(4,15)(5,16)(6,23)(7,17)(8,18)(10,25)(11,26)(12,28)(13,27)(14,19)(20,30)(21,32)(22,29)(24,31);(1,4)(2,10)(3,15)(5,12)(6,24)(7,20)(8,11)(9,25)(13,21)(14,29)(16,28)(17,30)(18,26)(19,22)(23,31)(27,32);(1,5,7,21,8,22,6,10)(2,11,12,24,13,4,19,20)(3,16,17,32,18,29,23,25)(9,26,28,31,27,15,14,30)3422 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 14466);