Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#336 ⋊ C2 |
| Sylow | C3 ⋊ C4×C22⋊C8 |
436 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 161 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 — 3 generators on 19 points:
(2,3)(4,6,7,5);(1,2,3)(9,11)(12,13,14,16,15,17,18,19);(4,5,7,6)(8,9)(10,11)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=e,f^2=g,b^a=bd,h^c=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10683136, #10683138, #10683140, … |
| maximal normal subgroup of | #10683136, #10683138, #10683140, … |
| maximal quotient of | #10685651, #10685655, #10685664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1175);