Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C25 |
| direct product | C59×#25562 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C22×D4×C59 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C4×D4×C59 ◁ G | |
1108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 4 generators on 87 points:
(2,4)(5,6)(7,11)(8,10)(9,12)(13,14,18,23)(15,21,26,20)(16,27,25,28)(17,24,19,22)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(5,7,8,12)(6,9,10,11)(13,15)(14,20)(16,19)(17,25)(18,26)(21,23)(22,28)(24,27);(1,2,3,4)(13,16,17,26,18,25,19,15)(14,21,22,28,23,20,24,27);(6,10)(9,11)(13,17,18,19)(14,22,23,24)(15,25,26,16)(20,28,21,27)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 18550);