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×C42 |
| direct product | C17×#2840 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C17 |
| prime radical | C25×C17 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
580 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(23,25)(26,27)(28,31)(29,30)(32,33)(36,40)(38,41);(20,24)(23,25)(27,30)(31,32)(34,35,37,39)(36,41,40,38);(18,19)(20,23)(21,22)(24,25)(26,28)(27,31)(29,33)(30,32)(34,36,37,40)(35,38,39,41);(18,20)(19,23)(21,24)(22,25)(26,27)(28,32)(29,30)(31,33)(34,35)(36,38)(37,39)(40,41)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1572);