Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#2104 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #401 |
| commutator, Frattini, cosocle | C24 | C23×C17 |
| prime radical | C24×C17 | C23 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C24×C17 ◁ G | |
178 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)(20,26,28,23)(21,24,30,33)(22,25)(27,32)(29,31);(18,20)(19,23)(21,29,30,27)(22,28)(24,32,33,31)(25,26);(18,21)(19,24,25,33)(20,27)(22,30)(23,31,26,32)(28,29)391 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 836);