Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60367 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C210 |
| direct product | C67×#60370 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C2×#585×C67 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×#41×C67 ◁ G | |
4746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 103 points:
(1,2)(3,4)(5,6,11,16)(7,17,20,30)(8,13,21,27)(9,15,10,14)(12,24,26,19)(18,31,32,36)(22,29,23,28)(25,34,35,33)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(5,7)(6,12)(8,18)(9,19)(10,24)(11,20)(13,25)(14,17)(15,30)(16,26)(21,32)(22,33)(23,34)(27,35)(28,31)(29,36);(2,4)(5,8)(6,13)(7,18)(9,22)(10,23)(11,21)(12,25)(14,28)(15,29)(16,27)(17,31)(19,33)(20,32)(24,34)(26,35)(30,36);(8,21)(13,27)(18,32)(22,23)(25,35)(28,29)(31,36)(33,34);(5,9,11,10)(6,14,16,15)(7,19,20,24)(8,22,21,23)(12,17,26,30)(13,28,27,29)(18,33,32,34)(25,31,35,36)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53358);