Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C8×Q8 ⋊ C2 |
| Sylow | C3 ⋊ #2988 |
432 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 217 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)(12,14,15,18)(13,17,16,19);(2,3)(13,16)(17,19);(2,3)(12,13)(14,17)(15,16)(18,19);(4,5,6,8,7,9,10,11)(13,16)(14,18)Polycyclic presentation:
2^7,3|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,h^b=h^2,h^c=h^2,h^d=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #10764620, #10764624, #10764631, … |
| maximal normal subgroup of | #10764620, #10764624, #10764631, … |
| maximal quotient of | #10793973, #10794074, #10794225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12482);