Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#18239 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C59×#3536 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C23×C4×C59 ◁ G | |
960 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2)(3,12)(4,9)(5,10)(6,15)(7,11)(8,13)(14,16)(17,18,21,24)(19,22,26,29)(20,23,27,30)(25,31,32,28)(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);(1,3,7,4)(2,8,11,16)(5,13,6,14)(9,15,12,10)(17,19)(18,22)(20,25)(21,26)(23,28)(24,29)(27,32)(30,31);(1,4,7,3)(2,9,11,12)(5,13,6,14)(8,15,16,10)(17,20)(18,23)(19,25)(21,27)(22,28)(24,30)(26,32)(29,31);(1,5,7,6)(2,10,11,15)(3,13,4,14)(8,9,16,12)2183 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 11227);