Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C23×C4 |
| direct product | C59×#33785 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C59 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,21)(12,20)(13,16)(14,27)(15,18)(17,24)(19,29)(22,38)(23,37)(25,32)(26,34)(28,36)(30,35)(31,39)(33,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3,4,8)(2,5,6,7)(10,16)(17,31)(18,20)(19,32)(21,37)(27,34)(33,36)(35,38);(3,8)(5,7)(9,11)(10,17)(12,22)(13,23)(14,28)(15,30)(16,31)(18,33)(19,35)(20,36)(21,27)(24,29)(25,39)(26,40)(32,38)(34,37);(2,6)(5,7)(9,12,13,15)(10,18,16,20)(11,22,23,30)(14,25,26,29)(17,33,31,36)(19,34,32,27)(21,35,37,38)(24,28,39,40)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 26773);