Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#61691 |
| 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 ◁ #532×C67 ◁ G | |
2046 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2)(3,7)(4,6)(5,8)(9,10,14,20)(11,22,25,16)(12,18,27,34)(13,21,15,19)(17,29,33,26)(23,37,39,31)(24,32,28,35)(30,40,36,38)(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)(9,11,14,25)(10,16,20,22)(12,23,27,39)(13,28,15,24)(17,30,33,36)(18,31,34,37)(19,35,21,32)(26,40,29,38);(9,12)(10,17)(11,23)(13,26)(14,27)(15,29)(16,30)(18,19)(20,33)(21,34)(22,36)(24,38)(25,39)(28,40)(31,35)(32,37);(3,8)(5,7)(9,12)(10,18)(11,23)(13,29)(14,27)(15,26)(16,31)(17,19)(20,34)(21,33)(22,37)(24,40)(25,39)(28,38)(30,35)(32,36);(2,6)(5,7)(9,13,14,15)(10,19,20,21)(11,24,25,28)(12,26,27,29)(16,32,22,35)(17,18,33,34)(23,38,39,40)(30,37,36,31)3283 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54679);