Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C26 |
| direct product | C67×#11032 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | #392 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C23×C4 | C23×C67 |
| socle | C2×C67 | #1438 |
| prime radical | C2×#575×C67 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C23×C4×C67 ◁ G | |
1252 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 3 generators on 99 points:
(1,2,6,10,7,11,5,12)(3,13,15,8,16,25,22,24)(4,17,19,27,21,9,20,28)(14,29,18,23,31,26,30,32)(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);(1,3)(2,8)(4,18)(5,22)(6,15)(7,16)(9,26)(10,25)(11,24)(12,13)(14,20)(17,29)(19,31)(21,30)(23,27)(28,32);(1,4)(2,9)(3,14)(5,19)(6,20)(7,21)(8,23)(10,27)(11,17)(12,28)(13,26)(15,30)(16,31)(18,22)(24,32)(25,29)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 4020);