Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2238 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#2239 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C23×C17 |
| prime radical | C23×C17 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×M16×C17 ◁ G | |
124 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 56 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)(18,19,23,27)(20,28,29,46)(21,32,33,49)(22,37,35,26)(24,39,40,30)(25,42,43,36)(31,44,38,47)(34,41,48,45);(21,33)(25,43)(28,46)(30,39)(32,49)(34,48)(36,42)(44,47);(18,20,22,38,23,29,35,31)(19,24,26,45,27,40,37,41)(21,34,36,39,33,48,42,30)(25,44,32,46,43,47,49,28)340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 971);