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×#61057 |
| 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 ◁ #525×C67 ◁ G | |
2696 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)(7,17,20,31)(8,13,23,30)(9,15,10,14)(12,24,27,19)(18,33,35,28)(21,36,34,26)(22,32,25,29)(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);(5,7,11,20)(6,12,16,27)(8,21,23,34)(9,19,10,24)(13,28,30,33)(14,17,15,31)(18,25,35,22)(26,32,36,29);(2,4);(5,8)(6,13)(7,18)(9,22)(10,25)(11,23)(12,26)(14,29)(15,32)(16,30)(17,33)(19,34)(20,35)(21,24)(27,36)(28,31);(5,9,11,10)(6,14,16,15)(7,19,20,24)(8,22,23,25)(12,17,27,31)(13,29,30,32)(18,34,35,21)(26,33,36,28)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54045);