Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C59 · Schur multiplier (H2) = C22×C4 |
| direct product | C59×#13193 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C59 | C2×D4 |
| commutator | C2×C4 | C22×C8×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| socle | C22×C59 | C2×C22⋊C8 |
| prime radical | C59×#532 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C59 ◁ C2×C4×C8×C59 ◁ G | |
446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 7552 |
A minimal faithful permutation representation — 3 generators on 95 points:
(2,4)(5,6,9,14,10,15,24,32,11,16,25,33,8,13,18,27)(7,17,20,34,19,29,35,31,21,30,23,36,22,12,26,28)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95);(5,7,18,35,8,22,25,20,11,21,24,26,10,19,9,23)(6,12,27,34,13,30,33,28,16,29,32,36,15,17,14,31);(1,2,3,4)4484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6181);