Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C67 · Schur multiplier (H2) = C28 |
| direct product | C2×C67×#3177 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C67 |
| prime radical | C24×C67 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ C2×#117×C67 ◁ G | |
1842 conjugacy classes of subgroups.
| minimal degree | μ(G) = 109 |
| transitive degree | μt(G) = 8576 |
A minimal faithful permutation representation — 5 generators on 109 points:
(1,2)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(3,4)(5,8)(6,7)(9,10)(11,12,16,20)(13,17,22,30)(14,24,27,39)(15,28,25,19)(18,32,33,26)(21,34,36,42)(23,38,35,31)(29,40,41,37);(4,7)(8,10)(11,13,16,22)(12,17,20,30)(14,21,27,36)(15,23,25,35)(18,29,33,41)(19,31,28,38)(24,34,39,42)(26,37,32,40);(11,14,25,32,16,27,15,26)(12,18,28,39,20,33,19,24)(13,21,35,40,22,36,23,37)(17,29,38,42,30,41,31,34);(3,5,6,9)(4,8,7,10)(13,22)(17,30)(21,36)(23,35)(29,41)(31,38)(34,42)(37,40)4288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 53669);