Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#61197 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #525×C67 ◁ G | |
2046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,16)(12,25)(13,18)(14,19)(15,20)(17,26)(21,35)(22,30)(23,34)(24,31)(27,32)(28,33)(29,36)(37,40)(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)(9,11,15,24)(10,16,20,31)(12,21,27,38)(13,22,14,23)(17,29,33,40)(18,30,19,34)(25,35,32,39)(26,36,28,37);(9,12)(10,17)(11,21)(13,26)(14,28)(15,27)(16,29)(18,32)(19,25)(20,33)(22,36)(23,37)(24,38)(30,39)(31,40)(34,35);(3,8)(5,7)(9,13,15,14)(10,18,20,19)(11,22,24,23)(12,26,27,28)(16,30,31,34)(17,32,33,25)(21,36,38,37)(29,39,40,35);(9,13,15,14)(10,19,20,18)(11,23,24,22)(12,26,27,28)(16,30,31,34)(17,25,33,32)(21,37,38,36)(29,39,40,35)3685 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54185);