Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C23 |
| direct product | C67×#32872 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #2826 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C2×#41×C67 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C22×C4×C67 ◁ G | |
482 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 131 points:
(1,2,7,12,8,14,6,13)(3,15,19,33,20,43,18,9)(4,21,25,10,26,36,24,37)(5,11,28,41,29,42,30,40)(16,31,22,34,48,57,47,44)(17,45,50,38,52,59,51,32)(23,39,27,35,53,61,54,62)(46,56,49,60,55,63,64,58)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131);(1,3,6,18,8,20,7,19)(2,9,12,15,14,33,13,43)(4,22,24,16,26,47,25,48)(5,17,28,50,29,52,30,51)(10,34,36,57,37,44,21,31)(11,38,40,45,42,32,41,59)(23,49,27,55,53,64,54,46)(35,58,39,63,62,60,61,56);(1,4,8,26)(2,10,14,37)(3,16,20,48)(5,27,29,54)(6,25,7,24)(9,31,33,57)(11,39,42,61)(12,21,13,36)(15,44,43,34)(17,49,52,64)(18,22,19,47)(23,30,53,28)(32,58,38,60)(35,41,62,40)(45,63,59,56)(46,51,55,50);(1,5)(2,11)(3,17)(4,23)(6,30)(7,28)(8,29)(9,32)(10,35)(12,41)(13,40)(14,42)(15,45)(16,46)(18,51)(19,50)(20,52)(21,39)(22,49)(24,54)(25,27)(26,53)(31,56)(33,38)(34,60)(36,61)(37,62)(43,59)(44,58)(47,64)(48,55)(57,63)1876 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 25860);