Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #1788 |
612 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 141 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)(12,14,16,15)(13,17,18,19);(12,13)(14,17)(15,19)(16,18);(2,3)(4,5,6,7)(8,9)(10,11)(13,17)(14,15)(18,19)Polycyclic presentation:
2^7,3|a^2=f,c^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,d^b=dg78 conjugacy classes — view the full character table.
| maximal subgroup of | #10687375, #10687376, #10687389, … |
| maximal normal subgroup of | #10687375, #10687376, #10687389, … |
| maximal quotient of | #10686563, #10686576, #10686637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4711);