Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ #3105 |
454 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 133 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 — 4 generators on 19 points:
(1,2,3)(4,6,7,10)(5,9,8,11);(13,17)(15,19)(16,18);(5,8)(9,11)(13,16)(17,18);(2,3)(4,5)(6,9)(7,8)(10,11)(12,13)(14,16)(15,17)(18,19)Polycyclic presentation:
2^7,3|d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,f^c=fg78 conjugacy classes — view the full character table.
| maximal subgroup of | #10690398, #10690404, #10765153, … |
| maximal normal subgroup of | #10690398, #10690404, #10765153, … |
| maximal quotient of | #10795192, #10798126, #10798170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14885);