Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#2984 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C24 |
| commutator | C22 | C23×C4×C17 |
| Frattini, cosocle | C2×C4 | C24×C17 |
| socle | C22×C17 | C23×C4 |
| prime radical | C23×C17 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
364 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 272 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,23,21,25,20,24)(26,27)(28,34)(29,32)(30,33)(31,36)(35,40)(37,39)(38,41);(18,20,21,22)(19,23,25,24)(26,28,30,36)(27,31,33,34)(29,37,38,35)(32,40,41,39);(18,20,21,22)(19,24,25,23)(26,29,30,38)(27,32,33,41)(28,35,36,37)(31,39,34,40);(19,25)(23,24)(27,33)(31,34)(32,41)(39,40)850 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1716);