Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#542 ⋊ C2 |
| Sylow | C3 ⋊ #3225 |
376 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)(5,9)(8,10)(12,15,16,17)(13,20,18,24)(14,21,23,25)(19,26,22,27);(2,3)(6,11)(8,10)(12,14)(13,19)(15,21)(16,23)(17,25)(18,22)(20,26)(24,27);(4,6,7,11)(5,8,9,10)(12,13)(14,22)(15,24)(16,18)(17,20)(19,23)(21,26)(25,27);(4,5)(6,10)(7,9)(8,11)(13,18)(14,21)(15,17)(19,26)(22,27)(23,25)Polycyclic presentation:
2^7,3|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3225, C2×#83464, #11666592, … |
| maximal normal subgroup of | D3×#3225, C2×#83464, #11666592, … |
| maximal quotient of | #10804566, #10804958, #10805792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16040);