Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#3483 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C13 |
| socle | C22×C13 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ G | |
1202 conjugacy classes of subgroups; only the 800 normal subgroups are shown.
This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 800 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19)(20,21)(22,23)(24,27)(25,29)(26,28);(14,15,18,19)(16,20,17,21)(22,24,27,23)(25,29,26,28);(14,16,18,17)(15,20,19,21)(22,25,27,26)(23,28,24,29);(14,16,18,17)(15,21,19,20)(22,26,27,25)(23,28,24,29);(14,17,18,16)(15,21,19,20)650 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2215);