Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C8×D4 ⋊ C2 |
| Sylow | C3 ⋊ #2988 |
432 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(2,3)(12,14,15,18)(13,17,16,19);(1,2,3)(13,16)(17,19);(12,13)(14,17)(15,16)(18,19);(4,5,6,8,7,9,10,11)(13,16)(14,18)Polycyclic presentation:
2^7,3|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,h^d=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #10764618, #10764622, #10764629, … |
| maximal normal subgroup of | #10764618, #10764622, #10764629, … |
| maximal quotient of | #10793973, #10793974, #10794072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11981);