Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#61338 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C2×#135×C67 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #533×C67 ◁ G | |
1732 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 107 points:
(2,5)(6,7)(9,10,14,18)(11,20,22,16)(12,24,26,34)(13,19,15,28)(17,29,33,25)(21,36,37,40)(23,32,27,31)(30,39,35,38)(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);(1,2,4,5)(3,7,8,6)(9,11,14,22)(10,16,18,20)(12,21,26,37)(13,27,15,23)(17,30,33,35)(19,32,28,31)(24,40,34,36)(25,39,29,38);(9,12)(10,17)(11,21)(13,25)(14,26)(15,29)(16,30)(18,33)(19,34)(20,35)(22,37)(23,38)(24,28)(27,39)(31,40)(32,36);(1,3,4,8)(2,6,5,7)(10,18)(11,22)(17,33)(19,28)(21,37)(23,27)(24,34)(38,39);(9,13,14,15)(10,19,18,28)(11,23,22,27)(12,25,26,29)(16,31,20,32)(17,34,33,24)(21,38,37,39)(30,40,35,36)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54326);