Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#1658 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C17 |
| prime radical | C17×#127 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
182 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)(19,24)(20,27)(21,22)(26,29)(28,30)(31,32)(35,39)(37,44)(40,48)(41,45)(42,46)(47,49);(18,19)(20,25)(21,29)(22,24)(23,26)(27,32)(28,33)(30,31)(34,35,38,41)(36,40,43,49)(37,45,44,39)(42,47,46,48);(18,20,23,28)(19,25,26,33)(21,27,22,30)(24,31,29,32)(34,36,38,43)(35,40,41,49)(37,46,44,42)(39,47,45,48)340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 390);