Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#11711500 |
4444 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 4444 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 22 points:
(4,6)(7,17,19)(8,15,13)(9,20,11)(10,12,14)(16,22,18);(3,4)(5,6)(8,12,13,17)(9,15,16,21)(11,18)(14,22,20,19);(1,2)64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72258610, C2×#72258617 |
| maximal normal subgroup of | C2×#72258617 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((4,6)(7,17,19)(8,15,13)(9,20,11)(10,12,14)(16,22,18), (3,4)(5,6)(8,12,13,17)(9,15,16,21)(11,18)(14,22,20,19), (1,2));