Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#61500 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #529×C67 ◁ G | |
1794 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 107 points:
(2,5)(6,8)(9,10)(11,20)(12,24)(13,18)(14,19)(15,29)(16,23)(17,26)(21,37)(22,33)(25,40)(27,35)(28,32)(30,36)(31,38)(34,39)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,2)(3,6)(4,5)(7,8)(9,11)(10,16)(12,25)(13,28)(14,23)(15,22)(17,34)(18,33)(19,20)(21,27)(24,37)(26,38)(29,32)(30,39)(31,36)(35,40);(9,12)(10,17)(11,21)(13,26)(14,27)(15,30)(16,31)(18,35)(19,36)(20,34)(22,38)(23,25)(24,29)(28,39)(32,40)(33,37);(2,5)(6,8)(9,13,14,15)(10,18,19,29)(11,22,23,28)(12,26,27,30)(16,32,20,33)(17,35,36,24)(21,38,25,39)(31,40,34,37);(1,3,4,7)(2,6,5,8)(11,23)(16,20)(21,25)(22,28)(31,34)(32,33)(37,40)(38,39)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54488);