Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #2361 |
788 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(12,14,15,13);(9,11);(2,3)(4,6,7,5)(13,14);(4,5,7,6)(8,9)(10,11)(12,13,15,14)Polycyclic presentation:
2^7,3|a^2=g,b^2=eg,d^2=e,b^a=be,c^a=cf,d^b=de,h^b=h^290 conjugacy classes — view the full character table.
| maximal subgroup of | #10815455, #10815464, #10815500, … |
| maximal normal subgroup of | #10815455, #10815464, #10815500, … |
| maximal quotient of | C22⋊C4×C4⋊Dic3, #10716685, #10716751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6043);