Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #2273 |
912 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 325 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) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(13,17)(16,18);(2,3)(14,19)(16,18);(8,9,10,11)(12,14)(13,16)(15,19)(17,18);(4,5,6,7)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,b^a=be,d^a=de,c^b=ce,h^c=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #10688645, #10692619, #10692621, … |
| maximal normal subgroup of | #10688645, #10692619, #10692621, … |
| maximal quotient of | #10716268, #10716269, #10716424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6136);