Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3585 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C67 · Schur multiplier (H2) = C29 |
| direct product | C67×#60113 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | C23×D4 |
| commutator | C4 | C24×C4×C67 |
| Frattini, cosocle | C2×C4 | C25×C67 |
| socle | C2×C67 | C23×C4⋊C4 |
| prime radical | C22×#41×C67 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C22×#41×C67 ◁ G | |
2564 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 5 generators on 99 points:
(1,2,6,10,7,11,5,20)(3,12,16,22,14,26,15,8)(4,9,19,24,17,23,18,30)(13,25,29,31,27,32,28,21)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3,5,15,7,14,6,16)(2,8,10,12,11,22,20,26)(4,13,18,28,17,27,19,29)(9,21,24,25,23,31,30,32);(1,4)(2,9)(3,13)(5,18)(6,19)(7,17)(8,21)(10,24)(11,23)(12,25)(14,27)(15,28)(16,29)(20,30)(22,31)(26,32);(4,17)(9,23)(13,27)(18,19)(21,31)(24,30)(25,32)(28,29);(3,14)(8,22)(12,26)(13,27)(15,16)(21,31)(25,32)(28,29)5494 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53101);