Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#61005 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C67×#3197 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×#117×C67 ◁ G | |
1672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 115 points:
(1,2)(3,9)(4,8)(5,7)(6,10)(11,15)(12,14)(13,16)(17,18,22,26)(19,27,28,40)(20,24,31,38)(21,33,35,25)(23,34,36,30)(29,41,42,48)(32,45,44,39)(37,46,47,43)(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)(2,6)(4,11)(5,10)(7,9)(8,13)(12,16)(14,15)(19,28)(23,36)(27,40)(29,42)(30,34)(37,47)(41,48)(43,46);(3,10)(6,9)(11,16)(13,15)(17,19,22,28)(18,23,26,36)(20,29,31,42)(21,34,35,30)(24,37,38,47)(25,40,33,27)(32,46,44,43)(39,48,45,41);(2,7)(6,9)(8,14)(13,15)(17,20)(18,24)(19,29)(21,32)(22,31)(23,37)(25,39)(26,38)(27,41)(28,42)(30,43)(33,45)(34,46)(35,44)(36,47)(40,48);(1,4,5,12)(2,8,7,14)(3,11,10,16)(6,13,9,15)(20,31)(24,38)(29,42)(32,44)(37,47)(39,45)(41,48)(43,46)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53993);