Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C22×C4 |
| direct product | C59×#13209 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C2×D8 |
| commutator | C2×C8 | C22×C4×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| socle | C22×C59 | C2×#102 |
| prime radical | C59×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
482 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 3 generators on 95 points:
(2,4)(5,6,9,14,11,15,10,25)(7,16,19,32,17,30,20,35)(8,21,22,27,24,36,23,13)(12,26,29,33,28,34,31,18)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(5,7,8,18,9,19,22,26,11,17,24,33,10,20,23,34)(6,12,27,30,25,31,21,32,15,28,13,16,14,29,36,35);(1,2,3,4)(7,17)(12,28)(16,30)(18,33)(19,20)(26,34)(29,31)(32,35)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6197);