Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C67 · Schur multiplier (H2) = C24 |
| direct product | C67×#9088 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | #386 |
| commutator | C2×C4 | C22×C8×C67 |
| Frattini, cosocle | C2×C42 | C23×C67 |
| prime radical | C23×C67 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
480 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 3 generators on 107 points:
(1,2,4,7,5,3,6,8)(9,10)(11,20)(12,24,27,34)(13,28)(14,18)(15,19)(16,22)(17,26,33,25)(21,36,38,30)(23,31)(29,32)(35,37,40,39)(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);(1,3,4,8,5,2,6,7)(9,11,13,22,15,23,14,29)(10,16,18,20,19,32,28,31)(12,21,26,39,27,38,25,37)(17,30,34,35,33,36,24,40);(9,12,15,27)(10,17,19,33)(11,21,23,38)(13,26,14,25)(16,30,32,36)(18,34,28,24)(20,35,31,40)(22,39,29,37)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 2076);