Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#441 ⋊ C2 |
| Sylow | C3 ⋊ #2950 |
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(9,16)(11,22)(14,28)(17,24)(18,31)(19,33)(23,35)(34,37);(4,6,7,5)(8,11,13,22)(9,15,16,30)(10,19,21,33)(12,23,26,35)(14,27,28,38)(17,29,24,36)(18,32,31,39)(20,34,25,37);(8,10,13,21)(9,14,16,28)(11,19,22,33)(12,25,26,20)(15,27,30,38)(17,31,24,18)(23,37,35,34)(29,39,36,32);(2,3)(4,5,7,6)(8,9)(10,18)(11,15)(12,24)(13,16)(14,20)(17,26)(19,32)(21,31)(22,30)(23,36)(25,28)(27,34)(29,35)(33,39)(37,38)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=fg,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^2,e^b=eg,d^c=dg,h^d=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10948650, D3×#2950, C2×#79831, … |
| maximal normal subgroup of | #10948650, D3×#2950, C2×#79831, … |
| maximal quotient of | #10764658, #10764882, #10765029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12407);