Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#2171 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | C2×D4 |
| commutator | C4 | C22×C8×C17 |
| Frattini, cosocle | C2×C8 | C23×C17 |
| socle | C2×C17 | C8×D4 |
| prime radical | C17×#135 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C2×C16×C17 ◁ G | |
144 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 92 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)(18,19,23,29,24,28,41,47,25,30,42,32,22,38,40,48)(20,31,34,36,33,26,43,37,27,44,46,35,39,45,49,21);(18,20)(19,26)(21,32)(22,39)(23,34)(24,33)(25,27)(28,44)(29,37)(30,45)(31,38)(35,47)(36,48)(40,49)(41,43)(42,46);(18,21,23,31,24,36,41,26,25,37,42,44,22,35,40,45)(19,27,29,46,28,39,47,49,30,20,32,34,38,33,48,43)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 903);