Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C43 |
| direct product | C67×#32817 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C22×D8×C67 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ #376×C67 ◁ G | |
746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 99 points:
(1,2,4,5)(3,6,7,8)(9,10,12,14)(11,13,15,16)(17,18,20,22)(19,25,27,23)(21,24,28,30)(26,31,29,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(2,5)(3,7)(9,11)(10,13)(12,15)(14,16)(18,22)(19,26)(21,28)(23,31)(25,32)(27,29);(3,7)(6,8)(10,14)(13,16)(17,19)(18,23)(20,27)(21,29)(22,25)(24,31)(26,28)(30,32);(1,3,4,7)(2,6,5,8)(11,15)(13,16)(18,22)(19,27)(24,30)(26,29)2278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 25805);