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 ⋊ #2972 |
500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(2,3)(13,17)(16,18);(1,2,3)(14,19)(16,18);(12,14)(13,16)(15,19)(17,18);(4,5,6,8,7,9,10,11)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=f,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, #10764620, #10764622, … |
| maximal normal subgroup of | #10764618, #10764620, #10764622, … |
| maximal quotient of | #10793857, #10793915, #10794072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12002);