Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3351 |
348 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3)(6,11)(9,10)(13,19)(17,25)(18,20)(24,26);(2,3)(4,7,8,5)(6,10,11,9)(13,18)(14,21)(15,23)(17,24)(19,20)(25,26);(4,6)(5,9)(7,10)(8,11)(12,14)(13,17)(15,22)(16,21)(18,26)(19,25)(20,24)(23,27);(4,5,8,7)(6,10,11,9)(12,13)(14,17)(15,18)(16,19)(20,23)(21,25)(22,26)(24,27)Polycyclic presentation:
2^7,3|a^2=e,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3351, C2×#83612, #11673944, … |
| maximal normal subgroup of | D3×#3351, C2×#83612, #11673944, … |
| maximal quotient of | #10811589, #10811621, #10812920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16188);