Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×C4×D4 ⋊ 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)(12,14,15,13);(9,11);(4,6,7,5)(13,14);(2,3)(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,h^a=h^2,d^b=de,h^d=h^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2361, C2×#82340, #10954746, … |
| maximal normal subgroup of | D3×#2361, C2×#82340, #10954746, … |
| maximal quotient of | C22⋊C4×Dic3⋊C4, #10716682, #10716685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14916);