Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#448 ⋊ C2 |
| Sylow | C3 ⋊ #3298 |
420 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)(6,11)(8,10);(12,13,15,17)(14,19,18,16);(2,3)(4,6)(5,8)(7,11)(9,10);(2,3)(4,5,7,9)(6,10,11,8)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|a^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,d^b=de,h^b=h^2,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3298, C2×#80049, #11671667, … |
| maximal normal subgroup of | D3×#3298, C2×#80049, #11671667, … |
| maximal quotient of | #10810612, #10811399, #10812337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12625);