Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ #2883 |
800 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 209 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 — 4 generators on 19 points:
(1,2,3)(7,15)(10,17)(13,19)(16,18);(2,3)(4,7)(5,10)(6,13)(8,15)(9,16)(11,17)(12,18)(14,19);(4,6)(5,9)(7,13)(8,14)(10,16)(11,12)(15,19)(17,18);(4,5)(6,12,14,9)(7,10)(8,11)(13,18,19,16)(15,17)Polycyclic presentation:
2^7,3|a^2=f,b^a=be,e^a=eg,f^b=fg,d^c=dg,h^c=h^263 conjugacy classes — view the full character table.
| maximal subgroup of | #10804334, #10804336, #10804337, … |
| maximal normal subgroup of | #10804334, #10804336, #10804337, … |
| maximal quotient of | #10761001, #10761004, #10761007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11264);