Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×C8×D4 ⋊ C2 |
| Sylow | C3 ⋊ #3335 |
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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)(6,11)(9,10);(2,3)(4,7,8,5)(6,10,11,9)(13,16)(15,19)(17,18);(4,6)(5,9)(7,10)(8,11);(2,3)(4,5,8,7)(6,10,11,9)(12,13,14,17)(15,16,19,18)Polycyclic presentation:
2^7,3|a^2=e,c^2=eg,f^2=g,b^a=beg,c^a=cf,f^a=fg,h^a=h^2,d^b=deg,f^c=fg,h^c=h^275 conjugacy classes — view the full character table.
| maximal subgroup of | #10784694, #10784701, #10784731, … |
| maximal normal subgroup of | #10784694, #10784701, #10784731, … |
| maximal quotient of | #10811402, #10811428, #10812807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11988);