Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1714 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#1722 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C17 |
| prime radical | C17×#127 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
198 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(20,23)(24,25)(26,27,30,33)(28,34,35,41)(29,37,38,32)(31,39,40,36);(26,28,29,36,30,35,38,39)(27,31,32,34,33,40,37,41);(18,19,23,25,21,24,20,22)(28,35)(31,40)(34,41)(36,39)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 454);