Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C27×C4 |
| direct product | C67×#60612 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| socle | C22×C67 | C23×D4 |
| prime radical | C67×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C2×#117×C67 ◁ G | |
2050 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)(3,6)(4,5)(7,8)(9,10)(11,21)(12,26)(13,18)(14,19)(15,20)(16,24)(17,28)(22,30)(23,32)(25,31)(27,34)(29,33)(35,38)(36,40)(37,39)(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);(2,5)(6,8)(9,11,14,25,15,23,13,24)(10,16,18,32,20,31,19,21)(12,22,28,38,29,36,27,37)(17,30,26,39,34,40,33,35);(1,3,4,7)(2,6,5,8)(9,12,13,27,15,29,14,28)(10,17,19,33,20,34,18,26)(11,22,24,37,23,36,25,38)(16,30,21,35,31,40,32,39);(11,23)(16,31)(21,32)(22,36)(24,25)(30,40)(35,39)(37,38);(9,13,15,14)(10,18,20,19)(11,24,23,25)(12,27,29,28)(16,32,31,21)(17,26,34,33)(22,37,36,38)(30,39,40,35)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53600);