Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C4×M16 ⋊ C2 |
| Sylow | C3 ⋊ #2956 |
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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)(10,14)(16,19)(17,18);(4,7,8,16,9,15,13,19)(5,10,12,18,6,14,11,17);(2,3)(4,6)(5,9)(7,14)(8,11)(10,15)(12,13)(16,17)(18,19);(2,3)(4,5,8,12,9,6,13,11)(7,10,16,18,15,14,19,17)Polycyclic presentation:
2^7,3|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^2,e^b=eg,h^b=h^2,d^c=dg84 conjugacy classes — view the full character table.
| maximal subgroup of | #10705265, #10705268, #10705270, … |
| maximal normal subgroup of | #10705265, #10705268, #10705270, … |
| maximal quotient of | #10764627, #10764638, #10764818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11117);