Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C2×C59×#2064 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C24×C59 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C23×C4×C59 ◁ G | |
1006 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 81 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81);(7,8,11,18,13,17,12,16)(9,15,19,14,10,21,20,22);(3,4)(5,6)(7,9,11,19,13,10,12,20)(8,14,16,15,17,22,18,21);(4,6)(7,10,13,9)(8,15,17,21)(11,19,12,20)(14,18,22,16)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 16588);