Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C29 |
| direct product | C67×#61096 |
| 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 | |
2686 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)(5,6,10,14)(7,12,17,29)(8,13,21,31)(9,22,25,15)(11,23,27,18)(16,28,34,30)(19,36,35,26)(20,33,24,32)(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)(6,11)(8,19)(9,23)(10,17)(12,22)(13,30)(14,27)(15,29)(16,20)(18,25)(21,35)(24,34)(26,32)(28,31)(33,36);(2,4)(5,7)(6,12)(8,16)(9,18)(10,17)(11,22)(13,28)(14,29)(15,27)(19,20)(21,34)(23,25)(24,35)(26,32)(30,31)(33,36);(5,8,10,21)(6,13,14,31)(7,16,17,34)(9,24,25,20)(11,26,27,36)(12,28,29,30)(15,33,22,32)(18,35,23,19);(6,14)(7,17)(13,31)(15,22)(16,34)(18,23)(19,35)(32,33)3685 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54084);