Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C59 · Schur multiplier (H2) = C210 |
| direct product | C2×C59×#2884 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×C22⋊C4 |
| commutator | C22 | C24×C4×C59 |
| Frattini, cosocle | C23 | C25×C59 |
| prime radical | C22×2−1+4×C59 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×Q8×C59 ◁ G | |
4818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 5 generators on 93 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(3,4)(5,13,16,9)(6,10)(7,11)(8,12)(14,27,30,21)(15,28,32,22)(17,23)(18,24)(19,25)(20,26)(29,34,31,33);(3,5)(4,9)(6,14)(7,15)(8,16)(10,21)(11,22)(12,13)(17,29)(18,30)(19,31)(20,32)(23,33)(24,27)(25,34)(26,28);(3,6,8,18)(4,10,12,24)(5,14,16,30)(7,19,20,17)(9,21,13,27)(11,25,26,23)(15,31,32,29)(22,34,28,33);(3,7,8,20)(4,11,12,26)(5,15,16,32)(6,17,18,19)(9,22,13,28)(10,23,24,25)(14,29,30,31)(21,33,27,34)4838 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 53057);