Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×C4×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #2366 |
832 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(12,14,15,13);(8,9,10,11);(4,6,7,5)(13,14);(2,3)(4,5,7,6)(9,11)(12,13,15,14)Polycyclic presentation:
2^7,3|a^2=g,b^2=eg,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^2,d^b=de90 conjugacy classes — view the full character table.
| maximal subgroup of | #10689598, #10689601, #10689603, … |
| maximal normal subgroup of | #10689598, #10689601, #10689603, … |
| maximal quotient of | C4⋊C4×C4⋊Dic3, #10716751, #10716755, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6229);