Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×C4×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #2354 |
632 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)(8,10,11,9);(12,15,16,14)(13,17,18,19);(2,3)(9,10)(12,14,16,15)(13,17,18,19);(4,5,6,7)(8,9,11,10)(12,13)(14,17)(15,19)(16,18)Polycyclic presentation:
2^7,3|a^2=g,b^2=f,c^2=f,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 | #10689367, #10689371, #10689395, … |
| maximal normal subgroup of | #10689367, #10689371, #10689395, … |
| maximal quotient of | #10716608, C4⋊C4×C4⋊Dic3, #10716670, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6214);