Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9103 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#11074 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #386 |
| commutator | C22×C4 | C22×C4×C59 |
| Frattini, cosocle | C23×C4 | C23×C59 |
| prime radical | C24×C59 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(2,4)(5,6,10,16,11,15,9,14)(7,12,18,26,19,27,24,31)(8,20,22,13,23,30,21,29)(17,32,33,28,34,36,35,25)(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);(1,2,3,4)(5,7)(6,12)(8,17)(9,24)(10,18)(11,19)(13,28)(14,31)(15,27)(16,26)(20,32)(21,35)(22,33)(23,34)(25,29)(30,36);(5,8,11,23)(6,13,15,29)(7,17,19,34)(9,22,10,21)(12,25,27,28)(14,30,16,20)(18,35,24,33)(26,36,31,32)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4062);