Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #2247 |
176 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3)(4,5,6,7);(2,3)(8,10,19,35,12,21,25,27,13,22,30,39,24,36,11,20)(9,14,23,33,16,28,31,34,17,29,38,37,26,32,15,18);(5,7)(8,9,13,17)(10,18,22,34)(11,23,25,38)(12,26,24,16)(14,27,29,20)(15,30,31,19)(21,37,36,33)(28,35,32,39)Polycyclic presentation:
2^7,3|a^2=g,b^2=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10708651, #10708652, #10708653, … |
| maximal normal subgroup of | #10708651, #10708652, #10708653, … |
| maximal quotient of | #10709843, #10709876, #10709878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3888);