Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C29 |
| direct product | C67×#61083 |
| 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 | |
2674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 103 points:
(1,2)(3,4)(5,6,11,16)(7,17,21,32)(8,13,23,30)(9,15,10,14)(12,25,28,20)(18,33,36,27)(19,34,35,26)(22,31,24,29)(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);(5,7,11,21)(6,12,16,28)(8,18,23,36)(9,20,10,25)(13,26,30,34)(14,17,15,32)(19,24,35,22)(27,31,33,29);(2,4)(5,8)(6,13)(7,18)(9,24)(10,22)(11,23)(12,26)(14,31)(15,29)(16,30)(17,33)(19,25)(20,35)(21,36)(27,32)(28,34);(5,8)(6,13)(7,19)(9,22)(10,24)(11,23)(12,27)(14,29)(15,31)(16,30)(17,34)(18,25)(20,36)(21,35)(26,32)(28,33);(5,9,11,10)(6,14,16,15)(7,20,21,25)(8,22,23,24)(12,17,28,32)(13,29,30,31)(18,19,36,35)(26,27,34,33)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54071);