Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#11109 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C67 | #390 |
| commutator | C22×C4 | C22×C4×C67 |
| Frattini, cosocle | C23×C4 | C23×C67 |
| socle | C2×C67 | #1439 |
| prime radical | C22×#41×C67 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C67 ◁ C23×C4×C67 ◁ G | |
852 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)(3,12)(4,16,18,26)(5,19)(6,10)(7,11)(8,14)(9,17,27,21)(13,25,31,22)(15,23)(20,24)(28,30,32,29)(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);(1,3,5,14,7,15,6,20)(2,8,10,12,11,24,19,23)(4,13,17,29,18,31,21,30)(9,25,26,32,27,22,16,28);(1,4)(2,9)(3,13)(5,17)(6,21)(7,18)(8,22)(10,26)(11,27)(12,28)(14,29)(15,31)(16,19)(20,30)(23,32)(24,25)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 4097);