Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#461 ⋊ C2 |
| Sylow | C3 ⋊ #3298 |
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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 — 4 generators on 19 points:
(1,2)(6,11)(8,10);(2,3)(12,13,15,17)(14,19,18,16);(2,3)(4,6)(5,8)(7,11)(9,10);(2,3)(4,5,7,9)(6,10,11,8)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|a^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,d^b=de,h^b=h^2,f^c=fg,h^c=h^2,h^d=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10784692, #10784696, #10784707, … |
| maximal normal subgroup of | #10784692, #10784696, #10784707, … |
| maximal quotient of | #10810622, #10811398, #10812334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13026);