Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #2308 |
1160 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 269 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) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(13,17)(16,18);(2,3)(9,11)(14,19)(16,18);(12,14)(13,16)(15,19)(17,18);(4,5,6,7)(8,9)(10,11)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^7,3|a^2=g,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10700573, #10700576, #10701515, … |
| maximal normal subgroup of | #10700573, #10700576, #10701515, … |
| maximal quotient of | #10716425, #10716430, #10716482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14697);