Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C59 · Schur multiplier (H2) = C24×C4 |
| direct product | C59×#25940 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C59 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C59 |
| prime radical | C22×D8×C59 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C59 ◁ C2×C4×Q8×C59 ◁ G | |
1098 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)(5,6,9,12)(7,11,8,10)(13,14,17,20)(15,21,23,28)(16,24,25,19)(18,26,27,22)(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);(5,7,9,8)(6,10,12,11)(15,22)(16,25)(18,21)(19,24)(23,26)(27,28);(1,2,3,4)(5,7,9,8)(6,11,12,10)(13,15,16,22,17,23,25,26)(14,18,19,21,20,27,24,28);(5,8,9,7)(6,11,12,10)(15,23)(18,27)(21,28)(22,26)2714 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 18928);