Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1414 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #354 |
| commutator | C42 | C2×C4×C17 |
| Frattini, cosocle | #124 | C22×C17 |
| prime radical | C2×D4×C17 | D4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×C4×C17 ◁ C17×#124 ◁ G | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28,30,43)(21,32,34,48)(22,36,38,26)(23,27)(24,29,39,46)(25,35)(31,45,37,44)(33,40,47,41)(42,49);(18,20)(19,24,27,41)(21,33)(22,37)(23,31)(25,28,42,45)(26,39,36,40)(29,34)(30,38)(32,43,48,44)(35,47)(46,49)289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 146);