Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#60346 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C25 |
| commutator | C22 | C24×C4×C67 |
| Frattini, cosocle | C2×C4 | C25×C67 |
| socle | C22×C67 | C24×C4 |
| prime radical | C67×#3531 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ G | |
1628 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 115 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18,21,26,22,24,33,38)(19,23,29,36,27,34,41,45)(20,25,31,40,32,37,44,47)(28,35,42,46,30,39,43,48)(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);(1,3,5,11)(2,6,8,9)(4,12,13,10)(7,15,16,14)(17,19)(18,23)(20,30)(21,29)(22,27)(24,34)(25,39)(26,36)(28,32)(31,43)(33,41)(35,37)(38,45)(40,48)(42,44)(46,47);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(18,24)(19,27)(25,37)(26,38)(28,30)(29,41)(40,47)(42,43);(2,8)(6,9)(7,16)(14,15)(19,27)(23,34)(28,30)(29,41)(35,39)(36,45)(42,43)(46,48);(17,20,21,31,22,32,33,44)(18,25,26,40,24,37,38,47)(19,28,29,42,27,30,41,43)(23,35,36,46,34,39,45,48)5092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53334);