Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #2333 |
596 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 181 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) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(9,13)(12,14)(16,18,19,22)(17,21,20,23);(10,15)(12,14)(17,20)(21,23);(4,6,7,5)(8,10,11,15)(9,12,13,14);(2,3)(4,5,7,6)(8,9)(10,14)(11,13)(12,15)(16,17)(18,21)(19,20)(22,23)Polycyclic presentation:
2^7,3|a^2=g,b^2=eg,d^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^2,c^b=ce84 conjugacy classes — view the full character table.
| maximal subgroup of | #10693231, #10693235, #10693245, … |
| maximal normal subgroup of | #10693231, #10693235, #10693245, … |
| maximal quotient of | #10716456, #10716522, #10716551, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6025);