Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#1776 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C2×D4 |
| commutator | C4 | C2×C42×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
272 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(26,27,29,31,30,32,28,33);(22,23,24,25)(27,31)(28,29)(32,33);(18,20,21,19)(27,32)(31,33)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 508);