Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1321 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #99 |
| commutator | C2×C4 | C2×C8×C17 |
| Frattini, cosocle | C2×M16 | C22×C17 |
| socle | C2×C17 | #323 |
| prime radical | C2×#41×C17 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×C4×C17 ◁ C2×M16×C17 ◁ G | |
112 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)(18,19,22,27,23,26,37,43,24,28,38,45,21,33,35,44)(20,29,31,46,30,25,39,40,32,42,36,48,34,41,47,49);(18,20)(19,25)(21,34)(22,36)(23,30)(24,32)(26,42)(27,40)(28,41)(29,33)(31,38)(35,39)(37,47)(43,48)(44,46)(45,49)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 53);