Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#3290 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ G | |
454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(20,29)(21,26)(22,39)(23,28)(24,32)(25,37)(27,40)(30,42)(31,48)(33,44)(34,43)(35,41)(36,46)(38,45)(47,49);(18,20)(19,24)(21,35)(22,33)(23,34)(25,42)(26,47)(27,43)(28,44)(29,39)(30,38)(31,36)(32,40)(37,49)(41,46)(45,48);(18,21)(19,25)(20,30)(22,36)(23,38)(24,41)(26,39)(27,45)(28,46)(29,48)(31,32)(33,49)(34,35)(37,40)(42,44)(43,47);(18,21)(19,26)(20,31)(22,37)(23,38)(24,42)(25,39)(27,46)(28,45)(29,48)(30,32)(33,35)(34,49)(36,40)(41,44)(43,47)493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 2022);