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×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #2349 |
704 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 237 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)(14,19)(16,18);(8,9,10,11)(13,17)(16,18);(2,3)(12,14)(13,16)(15,19)(17,18);(2,3)(4,5,6,7)(9,11)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=g,c^2=ef,b^a=be,c^a=cf,h^a=h^2,d^b=de,h^b=h^2,h^d=h^290 conjugacy classes — view the full character table.
| maximal subgroup of | #10688752, #10688757, #10691093, … |
| maximal normal subgroup of | #10688752, #10688757, #10691093, … |
| maximal quotient of | #10716621, #10716631, D12×#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6346);