Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32944 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C23×C4 |
| direct product | C67×#33065 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C2×#41×C67 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(3,6)(4,5)(7,8)(9,10,16,22)(11,18,25,32)(12,17,24,33)(13,27,30,35)(14,21,15,20)(19,29,36,28)(23,37,39,31)(26,34,38,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(2,5)(6,8)(9,11,14,12,16,25,15,24)(10,17,20,18,22,33,21,32)(13,23,28,26,30,39,29,38)(19,31,27,34,36,37,35,40);(1,3,4,7)(2,6,5,8)(9,12,14,25,16,24,15,11)(10,18,20,33,22,32,21,17)(13,26,28,39,30,38,29,23)(19,34,27,37,36,40,35,31);(9,13)(10,19)(11,23)(12,26)(14,28)(15,29)(16,30)(17,31)(18,34)(20,27)(21,35)(22,36)(24,38)(25,39)(32,40)(33,37)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26053);