Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C29 |
| direct product | C67×#61086 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #532×C67 ◁ G | |
2666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 103 points:
(1,2)(3,4)(5,6)(7,15)(8,12)(9,23)(10,13)(11,18)(14,26)(16,24)(17,33)(19,31)(20,34)(21,32)(22,29)(25,30)(27,36)(28,35)(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);(5,7,10,19)(6,11,13,16)(8,20,22,36)(9,24,26,18)(12,28,29,33)(14,31,23,15)(17,25,35,21)(27,32,34,30);(2,4)(5,6)(7,16)(8,12)(9,14)(10,13)(11,19)(15,24)(17,34)(18,31)(20,33)(21,30)(22,29)(23,26)(25,32)(27,35)(28,36);(5,8,10,22)(6,12,13,29)(7,17,19,35)(9,25,26,21)(11,27,16,34)(14,32,23,30)(15,33,31,28)(18,36,24,20);(6,13)(11,16)(12,29)(14,23)(15,31)(27,34)(28,33)(30,32)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54074);