Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#489 ⋊ C2 |
| Sylow | C3 ⋊ #3136 |
404 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)(13,19)(17,24)(18,25)(23,27);(2,3)(5,9)(8,11)(12,14,15,20,16,21,22,26)(13,18,17,23,19,25,24,27);(4,6,7,10)(5,8,9,11)(12,13,15,17,16,19,22,24)(14,18,20,23,21,25,26,27);(4,5)(6,8)(7,9)(10,11)(13,17)(14,20)(15,22)(18,25)(19,24)(21,26)Polycyclic presentation:
2^7,3|b^2=f,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,h^c=h^2,h^d=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3136, C2×#81680, #11664444, … |
| maximal normal subgroup of | D3×#3136, C2×#81680, #11664444, … |
| maximal quotient of | #10795392, #10797832, #10797852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14256);