Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2032 |
278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 278 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) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,7)(5,10)(6,12)(8,16)(9,17)(11,14)(13,15)(18,19);(4,6)(5,9)(7,15,16,12)(8,13)(10,17,14,19)(11,18);(2,3)(4,5)(6,9)(7,14,16,10)(8,11)(12,19,15,17)(13,18)Polycyclic presentation:
2^7,3|a^2=d,b^2=d,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,f^b=fg,d^c=dg45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2032, C2×#70025, #10822627, … |
| maximal normal subgroup of | D3×#2032, C2×#70025, #10822627, … |
| maximal quotient of | #10698333, #10698335, #10698337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2601);