Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3398 |
350 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)(4,7,8,6)(5,10,9,11);(2,3)(4,6,8,7)(5,10,9,11)(13,18)(14,21)(15,23)(17,24)(19,20)(25,26);(4,5,8,9)(6,10,7,11)(12,14)(13,17)(15,22)(16,21)(18,26)(19,24)(20,25)(23,27);(2,3)(5,9)(10,11)(12,13,16,20)(14,17,21,25)(15,18,23,19)(22,26,27,24)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,c^2=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,c^b=cg,d^b=de,f^c=fg,h^c=h^2,h^d=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3398, C2×#80590, #11676222, … |
| maximal normal subgroup of | D3×#3398, C2×#80590, #11676222, … |
| maximal quotient of | #10812015, #10812040, #10814044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13166);