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 ⋊ C4×#107 |
280 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 129 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) = 384 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(8,10,11,9);(1,2,3)(4,5,6,7)(13,16)(14,19)(17,18);(8,9,11,10)(12,13,14,17,15,18,19,16)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=deg,d^2=g,e^2=g,b^a=bd,d^b=dg,e^b=eg,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10705593, #10705597, #10705609, … |
| maximal normal subgroup of | #10705593, #10705597, #10705609, … |
| maximal quotient of | #10686371, #10686379, #10686398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1361);