Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#2070 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C23×C17 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(18,19,22,36,23,27,38,26)(20,28,30,24,31,44,48,40)(21,32,34,41,35,25,37,42)(29,45,46,39,33,43,47,49);(18,20,22,30,23,31,38,48)(19,24,26,28,27,40,36,44)(21,33,34,47,35,29,37,46)(25,39,41,45,32,49,42,43);(18,21,23,35)(19,25,27,32)(20,29,31,33)(22,37,38,34)(24,39,40,49)(26,42,36,41)(28,43,44,45)(30,47,48,46)391 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 802);