Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×C4×C8 ⋊ C2 |
| Sylow | C3 ⋊ #1476 |
276 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 101 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:
(1,2,3)(12,14,15,19)(13,16,18,17);(2,3)(12,13)(14,16)(15,18)(17,19);(2,3)(4,5,6,8,7,9,10,11)(12,13,14,16,15,18,19,17)Polycyclic presentation:
2^7,3|a^2=e,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^2,d^b=df,h^b=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10685858, #10685860, #10685863, … |
| maximal normal subgroup of | #10685858, #10685860, #10685863, … |
| maximal quotient of | #10683127, #10683135, #10683137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2310);