Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#1454 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | C23 |
| commutator | C22 | C2×C42×C17 |
| Frattini, cosocle | C42 | C23×C17 |
| socle | C22×C17 | C2×C42 |
| prime radical | C23×C17 | C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ G | |
178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(18,19,21,25,22,24,28,31)(20,23,27,29,26,30,32,33)(34,35)(36,39)(37,41)(38,40)(42,46)(43,45)(44,47)(48,49);(18,20)(19,23)(21,27)(22,26)(24,30)(25,29)(28,32)(31,33)(34,36,37,42,38,43,44,48)(35,39,41,46,40,45,47,49);(19,24)(20,26)(25,31)(27,32)(35,40)(39,45)(41,47)(46,49)952 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 186);