Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C29 |
| direct product | C67×#61091 |
| 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 ◁ #532×C67 ◁ G | |
2650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 103 points:
(1,2)(3,4)(5,6,12,17)(7,18,22,34)(8,9,14,27)(10,16,11,15)(13,29,33,21)(19,20,23,36)(24,30,28,26)(25,35,31,32)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(5,7,12,22)(6,13,17,33)(8,23,14,19)(9,25,27,31)(10,21,11,29)(15,18,16,34)(20,30,36,26)(24,35,28,32);(2,4)(5,8,12,14)(6,9,17,27)(7,19,22,23)(10,28,11,24)(13,31,33,25)(15,30,16,26)(18,20,34,36)(21,35,29,32);(5,9)(6,14)(7,20)(8,17)(10,26)(11,30)(12,27)(13,32)(15,28)(16,24)(18,23)(19,34)(21,31)(22,36)(25,29)(33,35);(5,10,12,11)(6,15,17,16)(7,21,22,29)(8,24,14,28)(9,26,27,30)(13,18,33,34)(19,32,23,35)(20,31,36,25)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54079);