Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60372 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C210 |
| direct product | C67×#60377 |
| 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 ◁ C22×#41×C67 ◁ G | |
4756 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)(5,6,11,15)(7,16,19,25)(8,13,10,23)(9,14,21,29)(12,24,27,17)(18,30,32,35)(20,28,22,33)(26,34,36,31)(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)(8,17)(9,18)(10,24)(11,19)(13,25)(14,26)(15,27)(16,23)(20,31)(21,32)(22,34)(28,35)(29,36)(30,33);(2,4)(5,8,11,10)(6,13,15,23)(7,17,19,24)(9,20,21,22)(12,25,27,16)(14,28,29,33)(18,31,32,34)(26,35,36,30);(5,9)(6,14)(7,18)(8,20)(10,22)(11,21)(12,26)(13,28)(15,29)(16,30)(17,31)(19,32)(23,33)(24,34)(25,35)(27,36);(9,21)(14,29)(18,32)(20,22)(26,36)(28,33)(30,35)(31,34)4087 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53365);