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×#2069 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C22×D4×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
216 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,25,22,26,21,30)(20,27,31,32,28,33,29,24);(18,20,21,29,22,28,23,31)(19,24,25,27,26,32,30,33);(20,28)(21,23)(25,30)(27,33)391 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 801);