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×#25558 |
| 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 | |
1102 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)(13,14,19,23)(15,20,24,21)(16,25,26,28)(17,22,18,27)(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)(16,17)(18,26)(19,24)(21,23)(22,25)(27,28);(1,2,3,4)(13,16,17,15,19,26,18,24)(14,21,27,28,23,20,22,25);(6,10)(9,11)(13,17,19,18)(14,22,23,27)(15,16,24,26)(20,25,21,28)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 18546);