Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #69507 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#127 ⋊ C2 |
| Sylow | C3 ⋊ #2011 |
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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)(9,11)(13,18)(14,15)(17,19);(5,7)(8,9)(10,11)(13,17)(14,15)(18,19);(2,3)(4,5)(6,7)(12,13)(14,17)(15,18)(16,19)Polycyclic presentation:
2^7,3|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,c^b=cf,d^b=dg,e^b=eg,d^c=dg,e^c=eg60 conjugacy classes — view the full character table.
| maximal subgroup of | #10683884, #10683887, #10683889, … |
| maximal normal subgroup of | #10683884, #10683887, #10683889, … |
| maximal quotient of | #10695607, #10695649, #10695717, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4343);