Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#60327 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C25 |
| commutator | C22 | C24×C4×C67 |
| Frattini, cosocle | C2×C4 | C25×C67 |
| socle | C22×C67 | C24×C4 |
| prime radical | C67×#3529 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ G | |
1812 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2)(3,7)(4,6)(5,8)(9,10,13,17,14,18,25,32)(11,15,21,28,19,26,33,37)(12,16,24,31,23,30,36,40)(20,27,34,38,22,29,35,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3)(2,5)(4,8)(6,7)(9,11)(10,15)(12,22)(13,21)(14,19)(16,29)(17,28)(18,26)(20,23)(24,35)(25,33)(27,30)(31,39)(32,37)(34,36)(38,40);(3,8)(5,7)(11,19)(12,23)(15,26)(16,30)(21,33)(24,36)(28,37)(31,40);(2,6)(5,7)(11,19)(15,26)(20,22)(21,33)(27,29)(28,37)(34,35)(38,39);(9,12,13,24,14,23,25,36)(10,16,17,31,18,30,32,40)(11,20,21,34,19,22,33,35)(15,27,28,38,26,29,37,39)5092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53315);