Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C59 · Schur multiplier (H2) = C26 |
| direct product | C2×C59×#2115 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C59 | C22⋊C4 |
| commutator | C22 | C23×C8×C59 |
| Frattini, cosocle | C2×C8 | C24×C59 |
| socle | C22×C59 | C2×C22⋊C8 |
| prime radical | C22×#41×C59 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C59 ◁ C23×C8×C59 ◁ G | |
1154 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 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);(3,4,6,11,7,12,18,26,8,10,19,23,20,24,31,33)(5,13,15,25,16,27,29,34,14,9,17,21,28,22,30,32);(3,5)(4,9)(6,17)(7,16)(8,14)(10,13)(11,25)(12,22)(15,19)(18,30)(20,28)(21,23)(24,27)(26,34)(29,31)(32,33);(5,14)(9,13)(15,17)(16,28)(21,25)(22,27)(29,30)(32,34)5192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26324);