Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C2×C17×#578 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D4 |
| commutator, Frattini, cosocle | C4 | C25×C17 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×#41×C17 ◁ G | |
1408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(3,4,8,12)(5,13,16,26)(6,10,17,24)(7,19,21,11)(9,20,23,15)(14,27,28,34)(18,31,30,25)(22,32,33,29);(3,5,8,16)(4,9,12,23)(6,14,17,28)(7,20,21,15)(10,22,24,33)(11,26,19,13)(18,32,30,29)(25,34,31,27);(3,6)(4,10)(5,14)(7,18)(8,17)(9,22)(11,25)(12,24)(13,27)(15,29)(16,28)(19,31)(20,32)(21,30)(23,33)(26,34);(6,17)(10,24)(14,28)(18,30)(22,33)(25,31)(27,34)(29,32)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2315);