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×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #2275 |
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 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) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2)(13,17)(16,18);(8,10,11,9)(14,19)(16,18);(2,3)(4,5,6,7)(12,14)(13,16)(15,19)(17,18);(2,3)(8,9,11,10)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=f,b^a=be,d^a=de,h^a=h^2,c^b=ce,h^b=h^2,h^d=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #10692081, #10692085, #10692095, … |
| maximal normal subgroup of | #10692081, #10692085, #10692095, … |
| maximal quotient of | #10716268, #10716272, #10716465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6327);