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 ⋊ #2339 |
928 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)(13,16)(17,19);(2,3)(9,11)(12,14,15,18)(13,17,16,19);(12,13)(14,17)(15,16)(18,19);(4,5,6,7)(8,9)(10,11)(13,16)(17,19)Polycyclic presentation:
2^7,3|a^2=g,c^2=e,b^a=be,c^a=cf,d^b=de,h^c=h^290 conjugacy classes — view the full character table.
| maximal subgroup of | #10810911, #10810912, #10810919, … |
| maximal normal subgroup of | #10810911, #10810912, #10810919, … |
| maximal quotient of | #10716592, #10716608, D4×C3⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14906);