Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10238 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C67 · Schur multiplier (H2) = C23 |
| direct product | C67×#10253 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C67 |
| prime radical | C23×C67 | #120 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
504 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 3 generators on 99 points:
(1,2)(3,11)(4,8)(5,14)(6,10)(7,12)(9,15)(13,16)(17,18,22,26)(19,27,29,32)(20,25,21,24)(23,30,31,28)(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);(1,3,6,4)(2,7,10,16)(5,13,15,12)(8,14,11,9)(17,19,22,29)(18,23,26,31)(20,30,21,28)(24,32,25,27);(1,4,6,3)(2,8,10,11)(5,12,15,13)(7,9,16,14)(18,24)(20,21)(23,27)(25,26)(28,30)(31,32)2479 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 3241);