Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1996 |
324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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 — 3 generators on 19 points:
(1,2,3)(12,14,15,19)(13,16,17,18);(2,3)(4,6)(5,8,9,11)(7,10);(4,5)(6,8,10,11)(7,9)(12,13,15,17)(14,18,19,16)Polycyclic presentation:
2^7,3|a^2=f,b^2=de,c^2=ef,b^a=bd,c^a=cef,d^a=dg,d^b=dg,e^b=eg,f^b=fg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10687391, #10687393, #10687398, … |
| maximal normal subgroup of | #10687391, #10687393, #10687398, … |
| maximal quotient of | #10695225, #10695229, #10695233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2105);