Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C3 ⋊ #1440 |
736 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(9,11)(13,15)(16,18,19,17);(12,13)(14,15)(16,17)(18,19);(2,3)(4,5,6,7)(8,9)(10,11)(17,18)Polycyclic presentation:
2^7,3|a^2=g,c^2=d,b^a=bd,c^a=ce,h^a=h^2,c^b=cf84 conjugacy classes — view the full character table.
| maximal subgroup of | #10682505, #10687762, #10687763, … |
| maximal normal subgroup of | #10682505, #10687762, #10687763, … |
| maximal quotient of | #10683109, #10683111, #10702756, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4124);