Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1909 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C67 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×C67×#1910 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | #386 |
| commutator | C2×C4 | C23×C4×C67 |
| Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C2×#535×C67 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G | |
1878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 2144 |
A minimal faithful permutation representation — 4 generators on 85 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85);(3,4)(5,11)(6,14,16,9)(7,13)(8,10)(12,15,18,17);(3,5,11,4,8,13,7,10)(6,12,15,9,16,18,17,14);(3,6)(4,9)(5,12)(7,17)(8,16)(10,14)(11,15)(13,18)3886 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 13996);