Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of D64 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C59 · Schur multiplier (H2) = C2 |
| direct product | C59×#7545 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C59 | D32 |
| commutator | C32 | C2×C4×C59 |
| Frattini, cosocle | C2×C32 | C22×C59 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C2×C4×C59 ◁ C2×C8×C59 ◁ C2×C16×C59 ◁ C2×C32×C59 ◁ G | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 15104 |
A minimal faithful permutation representation — 2 generators on 127 points:
(1,2,3,4)(6,12)(7,13)(8,18)(9,22)(10,25)(14,36)(15,40)(16,43)(17,31)(19,47)(20,50)(21,35)(23,52)(24,46)(26,51)(27,28)(29,37)(30,41)(32,33)(34,48)(38,65)(39,63)(42,66)(44,45)(49,68)(53,62)(54,61)(55,57)(56,67)(58,64)(59,60)(69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127);(5,6,13,28,8,14,32,40,22,37,47,62,45,54,20,30,10,16,34,56,23,38,49,58,26,42,60,63,46,55,21,31,11,17,35,57,24,39,59,66,51,64,68,65,52,67,48,43,25,41,50,61,44,53,19,29,9,15,33,36,18,27,7,12)4130 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 533);