Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1355 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#1356 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #329 |
| commutator | C42 | C2×C4×C17 |
| Frattini, cosocle | #97 | C22×C17 |
| prime radical | C22×C17 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C17×#97 ◁ G | |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,26,22,27,35,45,23,28,34,46,37,25,42,43)(20,29,30,47,31,24,38,39,32,40,48,44,36,41,33,49);(18,20,23,32)(19,24,28,41)(21,33,34,38)(22,36,37,31)(25,40,27,29)(26,44,46,47)(30,35,48,42)(39,43,49,45)340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 88);