Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #2321 |
808 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(13,17)(16,18);(2,3)(9,11)(14,19)(16,18);(4,6,7,5)(12,14)(13,16)(15,19)(17,18);(2,3)(4,5,7,6)(8,9)(10,11)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,b^a=be,c^a=cf,d^a=de,h^a=h^2,c^b=ce,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10690721, #10690731, #10801192, … |
| maximal normal subgroup of | #10690721, #10690731, #10801192, … |
| maximal quotient of | #10716425, #10716472, #10716482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6145);