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⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #3247 |
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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:
(1,2,3)(4,6,7,10)(5,9,8,11)(12,13,15,16)(14,17,19,18);(2,3)(5,8)(9,11)(12,14)(13,17)(15,19)(16,18);(4,5)(6,9)(7,8)(10,11)(12,13,15,16)(14,18,19,17);(2,3)(5,8)(6,10)(13,16)(14,17)(18,19)Polycyclic presentation:
2^7,3|b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^2,c^b=ce,f^c=fg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10772285, #10772287, #10772300, … |
| maximal normal subgroup of | #10772285, #10772287, #10772300, … |
| maximal quotient of | #10805093, #10805100, #10805575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11604);