Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17405 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C25×C4 |
| direct product | C67×#21751 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C67 |
| Frattini, cosocle | C24 | C24×C67 |
| prime radical | C22×#41×C67 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C23×Q8×C67 ◁ G | |
1294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(3,7)(4,6)(5,8)(9,10)(11,15)(12,22,24,16)(13,17)(14,18)(19,33,35,27)(20,28)(21,29)(23,36,38,30)(25,31)(26,32)(34,40,37,39)(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);(1,3)(2,5)(4,8)(6,7)(9,11,14,21)(10,15,18,29)(12,19,24,35)(13,25,26,20)(16,27,22,33)(17,31,32,28)(23,37,38,34)(30,40,36,39);(3,8)(5,7)(9,12)(10,16)(11,19)(13,23)(14,24)(15,27)(17,30)(18,22)(20,34)(21,35)(25,37)(26,38)(28,39)(29,33)(31,40)(32,36);(2,6)(5,7)(9,13,14,26)(10,17,18,32)(11,20,21,25)(12,23,24,38)(15,28,29,31)(16,30,22,36)(19,34,35,37)(27,39,33,40)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 14739);