Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#441 ⋊ C2 |
| Sylow | C3 ⋊ #3312 |
376 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2)(6,11)(8,10);(12,15,17,24)(13,19,20,27)(14,21,16,23)(18,26,25,22);(2,3)(4,6)(5,8)(7,11)(9,10)(12,14,17,16)(13,18,20,25)(15,23,24,21)(19,22,27,26);(2,3)(4,5,7,9)(6,10,11,8)(12,13)(14,18)(15,22)(16,25)(17,20)(19,21)(23,27)(24,26)Polycyclic presentation:
2^7,3|a^2=e,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,c^b=cg,d^b=de,h^b=h^2,f^c=fg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3312, C2×#79841, #11671967, … |
| maximal normal subgroup of | D3×#3312, C2×#79841, #11671967, … |
| maximal quotient of | #10810762, #10811480, #10812245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12417);