Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#23998 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C59 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C59 ◁ C22×C4×C59 ◁ G | |
1266 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 944 |
A minimal faithful permutation representation — 4 generators on 75 points:
(1,2)(3,9)(4,13)(5,8)(6,12)(7,15)(10,14)(11,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75);(1,2)(3,10,11,6)(4,7)(5,8)(9,12,16,14)(13,15);(1,3)(2,6)(4,14)(5,11)(7,16)(8,10)(9,13)(12,15);(4,15)(7,13)(9,16)(12,14)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 16986);