Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C27×C4 |
| direct product | C67×#60627 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C67×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C4×#41×C67 ◁ G | |
1998 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2)(3,6)(4,5)(7,8)(9,10,16,22)(11,18,25,31)(12,17,24,32)(13,19,27,34)(14,21,15,20)(23,33,37,40)(26,30,38,39)(28,36,29,35)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(2,5)(6,8)(9,11,14,12,16,25,15,24)(10,17,20,18,22,32,21,31)(13,23,28,26,27,37,29,38)(19,30,35,33,34,39,36,40);(1,3,4,7)(2,6,5,8)(9,12,14,25,16,24,15,11)(10,18,20,32,22,31,21,17)(13,26,28,37,27,38,29,23)(19,33,35,39,34,40,36,30);(9,13)(10,19)(11,23)(12,26)(14,28)(15,29)(16,27)(17,30)(18,33)(20,35)(21,36)(22,34)(24,38)(25,37)(31,40)(32,39);(13,27)(19,34)(23,37)(26,38)(28,29)(30,39)(33,40)(35,36)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53615);