Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#3131 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| socle | C22×C17 | C22×D4 |
| prime radical | C17×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
400 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27)(28,34)(29,33)(30,35)(31,36)(32,37)(38,41)(39,40);(19,22)(23,25)(26,28,31,38,32,39,30,29)(27,33,35,40,37,41,36,34);(18,20,21,24)(19,23,22,25)(26,29,30,39,32,38,31,28)(27,34,36,41,37,40,35,33);(26,30,32,31)(27,35,37,36)(28,29,39,38)(33,40,41,34)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 1863);