Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#421 ⋊ C2 |
| Sylow | C3 ⋊ #2955 |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3)(5,13)(11,25)(12,27)(14,22)(15,26)(24,34)(28,32)(29,35);(2,3)(4,7,9,20,10,21,8,19)(5,12,14,28,13,27,22,32)(6,16,17,30,18,31,23,33)(11,24,26,35,25,34,15,29);(4,6)(5,11)(7,16)(8,23)(9,17)(10,18)(12,24)(13,25)(14,26)(15,22)(19,33)(20,30)(21,31)(27,34)(28,35)(29,32);(4,5,9,14,10,13,8,22)(6,15,17,11,18,26,23,25)(7,12,20,28,21,27,19,32)(16,29,30,24,31,35,33,34)Polycyclic presentation:
2^7,3|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10801144, #10801146, #10801152, … |
| maximal normal subgroup of | #10801144, #10801146, #10801152, … |
| maximal quotient of | #10764597, #10764606, #10764608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11565);