Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#61186 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C67×#3486 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ #525×C67 ◁ G | |
2022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4288 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2,4,6)(3,7,8,5)(9,10)(11,19)(12,23)(13,17)(14,27)(15,21)(16,25)(18,26)(20,35)(22,30)(24,32)(28,31)(29,39)(33,37)(34,38)(36,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(1,3)(2,5)(4,8)(6,7)(9,11)(10,15)(12,20)(13,21)(14,22)(16,29)(17,19)(18,30)(23,40)(24,36)(25,37)(26,38)(27,34)(28,39)(31,33)(32,35);(9,12,13,24)(10,16,17,31)(11,20,21,36)(14,28,26,25)(15,29,19,33)(18,32,27,23)(22,39,38,37)(30,35,34,40);(3,8)(5,7)(11,21)(15,19)(20,36)(22,38)(29,33)(30,34)(35,40)(37,39);(10,17)(11,21)(16,31)(18,27)(20,36)(22,38)(23,32)(37,39)3685 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54174);