Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#2110 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | C42 |
| commutator | C4 | C2×C42×C17 |
| Frattini, cosocle | C2×C8 | C23×C17 |
| socle | C2×C17 | C2×#97 |
| prime radical | C23×C17 | M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ G | |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,25,22,27,33,41,23,26,34,40,35,42,48,49)(20,28,30,44,31,37,46,39,29,43,32,47,45,24,36,38);(18,20)(19,24,26,37)(21,32)(22,31)(23,29)(25,39,40,38)(27,28,42,43)(30,34)(33,36)(35,45)(41,47,49,44)(46,48);(20,29)(24,37)(28,43)(30,32)(31,45)(36,46)(38,39)(44,47)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 842);