Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Fitting | C3×C82 ⋊ C2 |
| Sylow | C3 ⋊ #1709 |
212 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,3)(4,6,7,5,9,10,8,11)(13,18)(17,25)(19,23)(20,26);(4,5,8,6,9,11,7,10)(12,14,15,21,16,22,24,27)(13,17,19,20,18,25,23,26);(2,3)(5,10)(6,11)(7,8)(12,13)(14,20)(15,23)(16,18)(17,21)(19,24)(22,26)(25,27)Polycyclic presentation:
2^7,3|b^2=dg,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #10681907, #10708587, #10708592, … |
| maximal normal subgroup of | #10681907, #10708587, #10708592, … |
| maximal quotient of | #10688964, #10694939, #10694950, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 636);