Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#2833 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(23,25)(26,27,30,31)(28,32,33,29)(35,39)(40,42)(41,45)(48,49);(20,24)(23,25)(28,33)(29,32)(34,35,38,39)(36,42,44,40)(37,45,47,41)(43,48,46,49);(18,19)(20,23)(21,22)(24,25)(26,28)(27,29)(30,33)(31,32)(34,36,38,44)(35,40,39,42)(37,46,47,43)(41,49,45,48);(18,20)(19,23)(21,24)(22,25)(26,29)(27,28)(30,32)(31,33)(34,37,38,47)(35,41,39,45)(36,43,44,46)(40,48,42,49)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1565);