Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32944 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24×C4 |
| direct product | C67×#33194 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C2×AGL(1,ℤ/8)×C67 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
980 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 103 points:
(2,4)(5,6,11,16)(7,17,18,28)(8,22,24,30)(9,15,10,14)(12,21,26,20)(13,25,29,23)(19,33,32,27)(31,35,36,34)(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);(5,7,9,20,11,18,10,21)(6,12,14,17,16,26,15,28)(8,19,23,34,24,32,25,35)(13,27,22,31,29,33,30,36);(1,2,3,4)(7,18)(12,26)(17,28)(19,32)(20,21)(27,33)(31,36)(34,35);(5,8)(6,13)(7,19)(9,23)(10,25)(11,24)(12,27)(14,22)(15,30)(16,29)(17,31)(18,32)(20,34)(21,35)(26,33)(28,36)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26182);