Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #2349 |
704 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(14,19)(16,18);(8,9,10,11)(13,17)(16,18);(12,14)(13,16)(15,19)(17,18);(2,3)(4,5,6,7)(9,11)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=g,c^2=ef,b^a=be,c^a=cf,h^a=h^2,d^b=de90 conjugacy classes — view the full character table.
| maximal subgroup of | #10688730, #10688734, #10688735, … |
| maximal normal subgroup of | #10688730, #10688734, #10688735, … |
| maximal quotient of | #10716620, #10716633, D4×C3⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14909);