Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #2249 |
184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 39 points:
(2,3)(4,5,6,7)(9,15)(14,27)(16,29)(17,26)(18,30)(23,38)(28,31)(32,37);(1,2,3)(8,10,19,33,13,22,25,36,12,21,34,39,24,35,11,20)(9,14,23,32,17,28,29,30,15,27,38,37,26,31,16,18);(5,7)(8,9)(10,18)(11,23)(12,15)(13,26)(14,20)(16,19)(17,24)(21,30)(22,37)(25,38)(27,36)(28,39)(29,34)(31,33)(32,35)Polycyclic presentation:
2^7,3|b^2=df,c^2=eg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10715985, #10715986, #10715992, … |
| maximal normal subgroup of | #10715985, #10715986, #10715992, … |
| maximal quotient of | #10709837, #10709846, #10709849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4041);