Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1745 |
272 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,3)(8,10,11,14)(9,13,12,15)(17,20)(21,23);(1,2,3)(4,5,6,7)(9,12)(13,15);(8,9)(10,13)(11,12)(14,15)(16,17,18,21,19,20,22,23)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,c^a=cg,h^c=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | #10683324, #10683326, #10683337, … |
| maximal normal subgroup of | #10683324, #10683326, #10683337, … |
| maximal quotient of | #10685611, #10685618, #10685623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1173);