Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×D4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #1490 |
316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(5,8)(9,11)(12,14,16,15)(13,18,19,17);(1,2,3)(13,17)(14,15)(18,19);(4,5,6,9,7,8,10,11)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=e,c^2=f,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cf,d^b=df,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1490, C2×#68175, #10761618, … |
| maximal normal subgroup of | D3×#1490, C2×#68175, #10761618, … |
| maximal quotient of | #10683316, #10683320, #10683324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 751);