Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#1873 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×D4 |
| commutator | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C24×C17 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ G | |
360 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 128 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 — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23)(24,25)(26,27,30,34,31,35,29,33)(28,36,37,32,39,40,38,41);(18,19,20,21)(26,28)(27,32)(29,37)(30,38)(31,39)(33,40)(34,36)(35,41);(23,25)(26,29,31,30)(27,33,35,34)(28,37,39,38)(32,40,41,36)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 605);