Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C59 · Schur multiplier (H2) = C23 |
| direct product | C2×C59×#1371 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C59 | D8 |
| commutator | C8 | C22×C8×C59 |
| Frattini, cosocle | C4×C8 | C23×C59 |
| socle, prime radical | C23×C59 | #107 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C59 ◁ C2×C42×C59 ◁ C2×C4×C8×C59 ◁ G | |
262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(3,4,5,7,6,8,9,10)(12,16)(13,17)(14,20)(18,26)(19,24)(21,25)(22,23);(11,12,17,23,14,18,21,24,15,19,25,26,20,22,13,16)5192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 4994);