Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#18881 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C67 |
| prime radical | #121×C67 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
844 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,6,9)(3,10,12,15)(4,8,5,13)(7,14,16,11)(17,18)(19,23)(20,30)(21,33)(22,25)(24,32)(26,36)(27,43)(28,41)(29,38)(31,42)(34,39)(35,40)(37,45)(44,47)(46,48)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(1,3)(2,7)(4,11)(5,14)(6,12)(8,15)(9,16)(10,13)(17,19,22,29)(18,23,25,38)(20,27,31,44)(21,34,36,28)(24,37,40,48)(26,41,33,39)(30,47,42,43)(32,46,35,45);(1,4,6,5)(2,8,9,13)(3,11,12,14)(7,15,16,10)(17,20)(18,24)(19,27)(21,35)(22,31)(23,37)(25,40)(26,42)(28,46)(29,44)(30,33)(32,36)(34,45)(38,48)(39,47)(41,43);(2,9)(3,12)(8,13)(11,14)(18,25)(23,38)(24,40)(26,33)(30,42)(37,48)(39,41)(43,47)2881 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 11869);