Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#102 ⋊ C2 |
| Sylow | C3 ⋊ #3318 |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(6,11)(8,10);(13,18)(14,16)(17,19);(2,3)(4,6)(5,8)(7,11)(9,10)(12,14,15,16)(13,17,19,18);(4,5,7,9)(6,10,11,8)(12,13,15,19)(14,17,16,18)Polycyclic presentation:
2^7,3|a^2=e,b^2=g,f^2=g,b^a=beg,c^a=cf,f^a=fg,c^b=cg,d^b=deg,h^b=h^2,f^c=fg57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3318, C2×#78764, #11671952, … |
| maximal normal subgroup of | D3×#3318, C2×#78764, #11671952, … |
| maximal quotient of | #10810723, #10811501, #10812284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11340);