Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4537 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1270 |
202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(12,14)(13,16)(15,19)(17,18)(21,24)(22,27)(25,26);(2,3)(4,5,6,8,7,9,10,11)(12,13)(14,18,19,16)(15,17)(20,21)(22,24)(23,26)(25,27)Polycyclic presentation:
2^7,3|a^2=d,c^2=f,d^2=g,b^a=bc,c^a=ce,h^a=h^2,c^b=cf,d^b=def66 conjugacy classes — view the full character table.
| maximal subgroup of | #10682545, #10682546, #10682612, … |
| maximal normal subgroup of | #10682545, #10682546, #10682612, … |
| maximal quotient of | #10681738, #10681931, #10681933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 215);