Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#61674 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C67×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #532×C67 ◁ G | |
2032 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)(9,10,15,20)(11,16,24,34)(12,18,26,36)(13,19,14,29)(17,28,37,25)(21,38,22,31)(23,32,27,33)(30,39,35,40)(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);(1,3)(2,5)(4,8)(6,7)(9,11)(10,16)(12,22)(13,27)(14,23)(15,24)(17,35)(18,31)(19,33)(20,34)(21,26)(25,39)(28,40)(29,32)(30,37)(36,38);(9,12)(10,17)(11,21)(13,25)(14,28)(15,26)(16,30)(18,29)(19,36)(20,37)(22,24)(23,39)(27,40)(31,33)(32,38)(34,35);(3,8)(5,7)(9,12)(10,18)(11,22)(13,28)(14,25)(15,26)(16,31)(17,29)(19,37)(20,36)(21,24)(23,39)(27,40)(30,33)(32,35)(34,38);(2,6)(5,7)(9,13,15,14)(10,19,20,29)(11,23,24,27)(12,25,26,28)(16,32,34,33)(17,36,37,18)(21,39,22,40)(30,38,35,31)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54662);