Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61109 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C29 |
| direct product | C67×#61111 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C22×C4×C67 ◁ G | |
2600 conjugacy classes of subgroups.
| minimal degree | μ(G) = 99 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 5 generators on 99 points:
(1,2)(3,12)(4,16)(5,9)(6,23)(7,10)(8,15)(11,24)(13,30)(14,18)(17,19)(20,29)(21,28)(22,27)(25,32)(26,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99);(1,3)(2,8)(4,10)(5,19)(6,16)(7,14)(9,26)(11,18)(12,23)(13,20)(15,24)(17,29)(21,31)(22,32)(25,28)(27,30);(1,4,7,8)(2,3,10,14)(5,17,22,25)(6,18,24,12)(9,13,27,31)(11,15,23,16)(19,29,32,28)(20,30,21,26);(1,5)(2,9)(3,13)(4,17)(6,21)(7,22)(8,25)(10,27)(11,29)(12,30)(14,31)(15,32)(16,19)(18,26)(20,24)(23,28);(2,10)(3,14)(9,27)(11,23)(13,31)(15,16)(19,32)(28,29)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54099);