Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×#73068 |
| derived | SL(2,𝔽3) ⋊ C2×C5×C8 |
254 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 254 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) = 29 |
| transitive degree | μt(G) = 640 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5)(14,28,23,21,24,29,18,19,25,15,16,27)(17,20,22,26);(6,7,8,10,9,11,12,13)(16,22)(17,24)(19,26)(20,28)(23,25)(27,29)320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236490);