Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#464 ⋊ C2 |
| Sylow | C3 ⋊ #3040 |
500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2)(8,11,12,13)(9,16,14,17)(10,19,20,21)(15,18,22,23);(2,3)(8,10)(9,15)(11,19)(12,20)(13,21)(14,22)(16,18)(17,23);(4,5,6,7)(9,14)(15,22)(16,17)(18,23);(5,7)(8,9)(10,18)(11,17)(12,14)(13,16)(15,19)(20,23)(21,22)Polycyclic presentation:
2^7,3|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,f^c=fg,h^c=h^2,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3040, C2×#80599, #11662056, … |
| maximal normal subgroup of | D3×#3040, C2×#80599, #11662056, … |
| maximal quotient of | #10779138, #10779147, #10779156, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13175);