Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #2875 |
556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(10,16)(14,19)(17,22)(21,23);(8,10)(9,14)(11,17)(12,16)(13,19)(15,21)(18,22)(20,23);(2,3)(4,5,6,7)(9,13)(14,19)(15,20)(21,23);(8,9,11,15,12,13,18,20)(10,14,17,21,16,19,22,23)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,e^2=g,b^a=bg,h^b=h^2,d^c=dg108 conjugacy classes — view the full character table.
| maximal subgroup of | #10710263, #10793765, #10793769, … |
| maximal normal subgroup of | #10710263, #10793765, #10793769, … |
| maximal quotient of | #10760778, #10760780, #10760797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16358);