Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#464 ⋊ C2 |
| Sylow | C3 ⋊ #3365 |
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:
(2,3)(4,6,7,11)(5,9,8,10);(1,2,3)(12,15,17,23)(13,19,20,27)(14,21,16,25)(18,26,24,22);(4,5,7,8)(6,10,11,9)(12,14,17,16)(13,18,20,24)(15,21,23,25)(19,26,27,22);(5,8)(9,10)(12,13,17,20)(14,18,16,24)(15,22,23,26)(19,25,27,21)Polycyclic presentation:
2^7,3|a^2=g,b^2=eg,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,f^c=fg,h^d=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3365, C2×#80581, #11674818, … |
| maximal normal subgroup of | D3×#3365, C2×#80581, #11674818, … |
| maximal quotient of | #10811796, #10812004, #10814142, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13157);