Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#461 ⋊ C2 |
| Sylow | C3 ⋊ D4×SD16 |
546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 546 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) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(8,10)(11,12)(13,15);(2,3)(5,7);(2,3)(8,9,12,14)(10,13,11,15);(2,3)(4,5)(6,7)(9,13)(10,11)(14,15)Polycyclic presentation:
2^7,3|b^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^2,d^b=de,e^b=eg,h^b=h^2,h^c=h^2,e^d=eg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10784547, #10784555, #10784562, … |
| maximal normal subgroup of | #10784547, #10784555, #10784562, … |
| maximal quotient of | #10784651, #10784666, #10784681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13024);