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×#61018 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | #535×C67 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C4×#41×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)(19,24)(20,30)(21,26)(22,36)(23,27)(25,28)(29,38)(31,40)(32,44)(33,37)(34,41)(35,42)(39,43)(45,48)(46,47)(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)(17,19,23,22)(18,24,27,36)(20,31,33,28)(21,34,35,29)(25,30,40,37)(26,41,42,38)(32,43,46,45)(39,47,48,44);(3,10)(6,9)(11,16)(13,15)(17,20,23,33)(18,25,27,40)(19,28,22,31)(21,32,35,46)(24,37,36,30)(26,39,42,48)(29,43,34,45)(38,47,41,44);(2,7)(6,9)(8,14)(13,15)(17,21)(18,26)(19,29)(20,32)(22,34)(23,35)(24,38)(25,39)(27,42)(28,43)(30,44)(31,45)(33,46)(36,41)(37,47)(40,48);(1,4,5,12)(2,8,7,14)(3,11,10,16)(6,13,9,15)(21,35)(26,42)(29,34)(32,46)(38,41)(39,48)(43,45)(44,47)3082 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54006);