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) = C42 |
| direct product | C17×#1747 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | C42 |
| commutator | C4 | C2×C42×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| socle | C2×C17 | #376 |
| prime radical | C23×C17 | #41 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ G | |
200 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)(20,28,31,41)(21,25)(22,26)(23,27)(24,30,36,44)(29,40,43,48)(32,37)(33,38)(34,39)(35,42,46,49)(45,47);(18,20)(19,24,27,36)(21,29)(22,30)(23,31)(25,35,38,46)(26,28,39,41)(32,42)(33,43)(34,44)(37,40,47,48)(45,49);(18,21,22,32,23,33,34,45)(19,25,26,37,27,38,39,47)(20,29,30,42,31,43,44,49)(24,35,28,40,36,46,41,48)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 479);