Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C3 ⋊ #1744 |
296 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(16,18,19,22)(17,21,20,23);(2,3)(4,5,6,7)(17,20)(21,23);(8,9,10,12,11,13,14,15)(16,17)(18,21)(19,20)(22,23)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^b=h^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #10682028, #10682030, C8×#815, … |
| maximal normal subgroup of | #10682028, #10682030, C8×#815, … |
| maximal quotient of | #10685610, #10685613, #10685614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2326);