Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#1304 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #95 |
| commutator | C23 | C42×C17 |
| Frattini, cosocle | C25 | C22×C17 |
| prime radical | C25×C17 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C25×C17 ◁ G | |
396 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26,28,31)(21,24)(22,25)(23,27,30,33)(29,32);(18,20)(19,23,25,31)(21,28)(22,27)(24,30,32,26)(29,33)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 36);