Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1284 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#1290 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #95 |
| commutator | C2×C4 | C42×C17 |
| Frattini, cosocle | C2×C42 | C22×C17 |
| prime radical | C23×C17 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
136 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,23,21,22,24,25)(26,27,29,34,31,35,30,33)(28,36,37,32,39,40,38,41);(19,22)(20,24)(26,28,30,38,31,39,29,37)(27,32,34,40,35,41,33,36)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 22);