Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#18446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
1032 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 1888 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,7)(3,11)(4,15)(8,21)(9,19)(10,16)(12,14)(13,28)(17,30)(20,25)(22,32)(23,29)(24,31)(26,27)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,2)(3,8)(4,16)(5,10)(6,9)(7,15)(11,25)(12,22)(13,29)(14,23)(17,31)(18,24)(19,30)(20,27)(21,28)(26,32);(3,12)(4,17)(7,19)(8,22)(11,14)(13,26)(15,30)(16,31)(20,21)(23,25)(27,28)(29,32);(1,3)(2,8)(4,13)(5,12)(6,14)(7,20)(9,23)(10,22)(11,18)(15,27)(16,29)(17,28)(19,32)(21,31)(24,25)(26,30)2006 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11434);