Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1795 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#1796 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #379 |
| commutator | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C2×C17×2−1+4 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
536 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 132 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)(20,28)(21,32,34,25)(22,35)(23,27)(24,30)(26,37)(29,43,45,42)(31,41)(33,40,49,47)(36,39)(38,44,46,48);(18,20,23,31)(19,24,27,39)(21,29,34,45)(22,36,37,30)(25,38,32,46)(26,41,35,28)(33,48,49,44)(40,43,47,42);(18,21)(19,25)(20,29)(22,33)(23,34)(24,38)(26,40)(27,32)(28,42)(30,44)(31,45)(35,47)(36,48)(37,49)(39,46)(41,43)493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 528);