Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#1902 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #386 |
| commutator | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C2×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
304 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 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)(21,33,36,43)(22,37)(23,27)(24,28)(25,31)(26,35,42,34)(30,45,47,39)(32,40)(38,41)(44,46,49,48);(18,20,22,31,24,32,23,38)(19,25,27,29,28,41,37,40)(21,30,35,48,36,47,34,46)(26,39,43,44,42,45,33,49);(18,21)(19,26)(20,30)(22,35)(23,34)(24,36)(25,39)(27,43)(28,42)(29,44)(31,48)(32,47)(33,37)(38,46)(40,49)(41,45)493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 634);