Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C67 · Schur multiplier (H2) = C29 |
| direct product | C67×#60176 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator | C4 | C24×C4×C67 |
| Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C2×#576×C67 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C4×#41×C67 ◁ G | |
2818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 87 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 87 points:
(1,2,4,3)(5,6,9,11)(7,12,14,18)(8,10,16,13)(15,17,20,19)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(6,10)(8,16)(11,13)(12,17)(15,20)(18,19);(1,3,4,2)(6,11)(10,13)(12,18)(17,19);(5,7)(6,12)(8,15)(9,14)(10,17)(11,18)(13,19)(16,20);(7,14)(12,18)(15,20)(17,19)5494 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53164);