Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C67 · Schur multiplier (H2) = C25 |
| direct product | C67×#33839 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C67 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C4×D4×C67 ◁ C8×D4×C67 ◁ G | |
712 conjugacy classes of subgroups.
| minimal degree | μ(G) = 103 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 4 generators on 103 points:
(1,2)(3,4)(5,6,10,15)(7,16,17,28)(8,21,24,30)(9,12,23,14)(11,26,27,19)(13,31,33,22)(18,34,35,29)(20,36,25,32)(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)(8,18)(9,25)(10,17)(12,29)(13,32)(14,34)(15,27)(16,21)(19,22)(20,23)(24,35)(26,31)(28,30)(33,36);(2,4)(7,17)(11,27)(16,28)(18,35)(19,26)(20,25)(29,34)(32,36);(6,12)(7,18)(8,22)(9,23)(11,28)(14,15)(16,27)(17,35)(19,20)(21,30)(24,31)(25,26)(29,32)(34,36)2881 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 26827);