Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#135 ⋊ C2 |
| Sylow | C3 ⋊ #3268 |
510 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(9,15)(11,19)(13,16)(14,21)(17,23)(20,22);(5,7)(8,10,12,18)(9,14,16,22)(11,17,19,23)(13,20,15,21);(8,9,12,16)(10,14,18,22)(11,15,19,13)(17,21,23,20);(2,3)(4,5)(6,7)(9,13)(11,19)(14,20)(15,16)(17,23)(21,22)Polycyclic presentation:
2^7,3|b^2=g,c^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,d^b=de,e^b=eg,e^d=eg57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3268, C2×#83922, #11670269, … |
| maximal normal subgroup of | D3×#3268, C2×#83922, #11670269, … |
| maximal quotient of | #10784594, #10784714, #10784864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16498);