Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#2884 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C22×C22⋊C4 |
| commutator | C22 | C23×C4×C17 |
| Frattini, cosocle | C23 | C24×C17 |
| prime radical | C2×C17×2−1+4 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×Q8×C17 ◁ G | |
716 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(18,19)(20,28,31,24)(21,25)(22,26)(23,27)(29,42,45,36)(30,43,47,37)(32,38)(33,39)(34,40)(35,41)(44,49,46,48);(18,20)(19,24)(21,29)(22,30)(23,31)(25,36)(26,37)(27,28)(32,44)(33,45)(34,46)(35,47)(38,48)(39,42)(40,49)(41,43);(18,21,23,33)(19,25,27,39)(20,29,31,45)(22,34,35,32)(24,36,28,42)(26,40,41,38)(30,46,47,44)(37,49,43,48);(18,22,23,35)(19,26,27,41)(20,30,31,47)(21,32,33,34)(24,37,28,43)(25,38,39,40)(29,44,45,46)(36,48,42,49)697 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1616);