Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C59 · Schur multiplier (H2) = C24 |
| direct product | C2×C59×#1395 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #99 |
| commutator | C2×C4 | C2×C42×C59 |
| Frattini, cosocle | C2×#41 | C23×C59 |
| socle | C22×C59 | #342 |
| prime radical | C22×#41×C59 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C22×C4×C59 ◁ C22×#41×C59 ◁ G | |
766 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 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)(5,13,15,25)(6,17,18,10)(7,20)(8,12)(9,14)(11,21)(16,30,29,26)(19,24,32,31)(22,34)(23,28)(27,33);(3,5,7,16,8,15,21,29)(4,9,11,22,12,23,20,33)(6,14,19,27,18,28,32,34)(10,13,24,26,17,25,31,30)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 5576);