Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#1312 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C17 | C22 |
| commutator | C2 | C4×C16×C17 |
| Frattini, cosocle | C4×C8 | C22×C17 |
| socle, prime radical | C22×C17 | C4×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C17 ◁ G | |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
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)(18,19,20,23,21,22,24,25);(19,22)(23,25)(26,27,28,31,29,32,34,37,30,33,35,38,36,39,40,41)1360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 44);