Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C26 |
| direct product | C59×#23514 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C59 | #120 |
| commutator, Frattini, cosocle | C24 | C24×C59 |
| socle | C22×C59 | C2×#120 |
| prime radical | C59×#3449 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C59 ◁ C23×C4×C59 ◁ G | |
1530 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 4 generators on 79 points:
(2,3)(5,6)(7,10)(8,11)(9,12)(13,17)(14,16)(15,18)(19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79);(1,2)(3,4)(5,7)(6,10)(8,13)(9,14)(11,17)(12,16)(15,19)(18,20);(1,3,4,2)(10,16)(17,20);(5,8,9,15)(6,11,12,18)(7,13,14,19)(10,17,16,20)3068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 16502);