Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12077 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C59 · Schur multiplier (H2) = C2×C4 |
| direct product | C59×#13141 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #442 |
| commutator | C2×C8 | C22×C4×C59 |
| Frattini, cosocle | C22×C8 | C23×C59 |
| prime radical | C23×C59 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ C2×#97×C59 ◁ G | |
320 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 3776 |
A minimal faithful permutation representation — 3 generators on 95 points:
(2,3)(5,6)(7,17)(8,20,22,28)(9,23)(10,12)(11,16)(13,18,31,36)(14,25)(15,19)(21,33,24,34)(26,32,35,30)(27,29)(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);(1,2,4,3)(5,7,9,10,11,19,25,27)(6,12,14,17,16,29,23,15)(8,18,24,26,22,36,21,35)(13,28,32,34,31,20,30,33);(1,3,4,2)(5,8,11,22)(6,13,16,31)(7,18,19,36)(9,24,25,21)(10,26,27,35)(12,28,29,20)(14,32,23,30)(15,33,17,34)2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 6129);