Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C17×#1275 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C42 |
| commutator | C4 | C4×C8×C17 |
| Frattini, cosocle | C2×C42 | C22×C17 |
| socle | C22×C17 | #95 |
| prime radical | C23×C17 | C4⋊C4 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 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)(28,35,37,41)(29,33)(30,39)(31,34)(32,36,40,38);(26,28,30,38,31,37,29,36)(27,32,33,35,34,40,39,41)748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 7);