Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C67×#61224 |
| 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 | |
2020 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 107 points:
(1,2,4,6)(3,7,8,5)(9,10,14,20)(11,18,24,16)(12,25,28,36)(13,21,15,19)(17,30,34,27)(22,37,26,40)(23,32,29,35)(31,39,33,38)(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)(9,11,14,24)(10,16,20,18)(12,26,28,22)(13,29,15,23)(17,33,34,31)(19,35,21,32)(25,37,36,40)(27,38,30,39);(9,12,14,28)(10,17,20,34)(11,22,24,26)(13,27,15,30)(16,31,18,33)(19,25,21,36)(23,38,29,39)(32,37,35,40);(3,8)(5,7)(9,11)(10,18)(12,22)(13,29)(14,24)(15,23)(16,20)(17,33)(19,32)(21,35)(25,37)(26,28)(27,39)(30,38)(31,34)(36,40);(9,13,14,15)(10,19,20,21)(11,23,24,29)(12,27,28,30)(16,32,18,35)(17,25,34,36)(22,38,26,39)(31,37,33,40)3484 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 54212);