Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#60318 |
| 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)(9,10,13,18,14,19,26,34)(11,15,22,28,20,16,29,31)(12,23,24,37,25,17,32,33)(21,30,36,40,35,27,38,39)(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)(12,21)(13,22)(14,20)(16,19)(17,27)(18,28)(23,30)(24,36)(25,35)(26,29)(31,34)(32,38)(33,39)(37,40);(3,8)(5,7)(9,11)(10,16)(12,21)(13,22)(14,20)(15,19)(17,30)(18,31)(23,27)(24,36)(25,35)(26,29)(28,34)(32,38)(33,40)(37,39);(2,6)(5,7)(11,20)(15,16)(21,35)(22,29)(27,30)(28,31)(36,38)(39,40);(9,12,13,24,14,25,26,32)(10,17,18,33,19,23,34,37)(11,21,22,36,20,35,29,38)(15,27,28,39,16,30,31,40)5092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53306);