Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C59 · Schur multiplier (H2) = C23 |
| direct product | C59×#12606 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | C2×C42 |
| commutator | C2×C4 | C2×C42×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| socle | C22×C59 | C2×#97 |
| prime radical | C24×C59 | M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ G | |
466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(1,2)(3,4)(5,6)(7,17,19,26)(8,14)(9,23)(10,16)(11,13)(12,18,27,21)(15,24)(20,34,33,31)(22,30)(25,29)(28,35,36,32)(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);(2,4)(5,7,9,20,10,21,25,35,11,19,24,33,8,18,22,32)(6,12,15,28,16,26,30,34,13,27,23,36,14,17,29,31);(6,13)(7,18,19,21)(9,24)(12,26,27,17)(14,16)(20,35,33,32)(22,25)(28,31,36,34)3776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 5594);