Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C4×#41 ⋊ C2 |
| Sylow | C3 ⋊ #3040 |
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(8,11,12,13)(9,16,14,17)(10,19,20,21)(15,18,22,23);(8,10)(9,15)(11,19)(12,20)(13,21)(14,22)(16,18)(17,23);(4,5,6,7)(9,14)(15,22)(16,17)(18,23);(2,3)(5,7)(8,9)(10,18)(11,17)(12,14)(13,16)(15,19)(20,23)(21,22)Polycyclic presentation:
2^7,3|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^2,f^c=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10692262, #10692264, #10692269, … |
| maximal normal subgroup of | #10692262, #10692264, #10692269, … |
| maximal quotient of | #10779141, #10779150, #10779159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15103);