Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#1683 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C17 |
| prime radical | C2×D4×C17 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
160 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 68 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 — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,22)(21,23)(24,25)(26,27,30,33)(28,34,37,41)(29,38,35,32)(31,39,40,36);(19,22)(23,24)(26,28,35,39,30,37,29,36)(27,31,38,41,33,40,32,34);(19,23)(21,25)(22,24)493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 415);