Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#2943 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D4 |
| commutator | C4 | C23×C4×C17 |
| Frattini, cosocle | C2×C4 | C24×C17 |
| socle | C22×C17 | C22×D4 |
| prime radical | C2×C17×#135 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
492 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23)(24,31)(25,30)(26,34)(27,29)(28,32)(33,37)(35,36);(22,24)(23,28)(25,32)(26,35)(27,33)(29,36)(30,37)(31,34);(18,20,21,19)(23,29)(28,36)(30,34)(31,37);(22,25,27,26)(23,30,29,34)(24,32,33,35)(28,37,36,31)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1675);