Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#121 ⋊ C2 |
| Sylow | C3 ⋊ #3194 |
466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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)(5,9)(8,10);(6,11)(8,10)(13,18)(14,15)(17,19);(4,6)(5,8)(7,11)(9,10)(12,14,16,15)(13,17,19,18);(2,3)(4,5)(6,10)(7,9)(8,11)(12,13)(14,17)(15,18)(16,19)Polycyclic presentation:
2^7,3|b^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^2,c^b=ceg,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10692142, #10692148, #10769337, … |
| maximal normal subgroup of | #10692142, #10692148, #10769337, … |
| maximal quotient of | #10804261, #10804271, #10805481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15204);