Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3349 |
336 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)(12,14,17,16)(13,18,20,25)(15,21,24,23)(19,26,27,22);(2,3)(4,7,8,5)(6,10,11,9)(12,15)(13,19)(14,21)(16,23)(17,24)(18,26)(20,27)(22,25);(4,6)(5,9)(7,10)(8,11)(12,14,17,16)(13,18,20,25)(15,23,24,21)(19,22,27,26);(2,3)(4,5,8,7)(6,10,11,9)(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=e,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,f^c=fg,h^c=h^257 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3349, C2×#79475, #11673840, … |
| maximal normal subgroup of | D3×#3349, C2×#79475, #11673840, … |
| maximal quotient of | #10811522, #10811552, #10812872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12051);