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×Q8 ⋊ C2 |
| Sylow | C3 ⋊ #2341 |
872 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 275 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(12,15,16,14)(13,18,17,19);(2,3)(9,11)(12,14,16,15)(13,18,17,19);(12,13,16,17)(14,18,15,19);(4,5,6,7)(8,9)(10,11)(13,17)(18,19)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,c^2=e,d^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 | #10810919, #10810920, #10810938, … |
| maximal normal subgroup of | #10810919, #10810920, #10810938, … |
| maximal quotient of | #10716608, Q8×C3⋊#95, #10716755, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15033);