Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#3233 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| prime radical | C17×#121 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26)(21,24)(22,25)(23,28)(27,32)(29,31)(30,33)(34,35)(36,44)(37,43)(38,40)(39,42)(41,46)(45,49)(47,48);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(35,40)(36,45)(42,43)(46,47);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(34,36,38,45)(35,41,40,48)(37,46,39,47)(42,44,43,49);(19,25)(23,26)(24,33)(31,32)(34,37,38,39)(35,42,40,43)(36,46,45,47)(41,44,48,49)544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1965);