Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#464 ⋊ C2 |
| Sylow | C3 ⋊ #3311 |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2)(6,11)(8,10)(12,14,17,16)(13,18,20,25)(15,21,24,23)(19,26,27,22);(2,3)(12,15)(13,19)(14,21)(16,23)(17,24)(18,26)(20,27)(22,25);(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,d^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^c=h^2,h^d=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3311, C2×#80617, #11671965, … |
| maximal normal subgroup of | D3×#3311, C2×#80617, #11671965, … |
| maximal quotient of | #10810749, #10811517, #10812301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13193);