Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#33662 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C67 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C67 |
| socle | C22×C67 | C22×D8 |
| prime radical | C67×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C67 ◁ C2×C42×C67 ◁ C2×C4×C8×C67 ◁ G | |
558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 4 generators on 107 points:
(1,2)(3,6)(4,5)(7,8)(9,10)(11,15)(12,16)(13,26)(14,19)(17,23)(18,24)(20,27)(21,36)(22,30)(25,32)(28,33)(29,34)(31,37)(35,39)(38,40)(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);(2,5)(6,8)(9,11,14,22)(10,15,19,30)(12,20,25,35)(13,21,24,34)(16,27,32,39)(17,28,31,38)(18,29,26,36)(23,33,37,40);(10,16)(12,23)(13,24)(15,27)(17,18)(19,32)(20,33)(21,34)(25,37)(26,31)(28,29)(30,39)(35,40)(36,38);(1,3,4,7)(2,6,5,8)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26650);