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 ⋊ #2957 |
452 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)(7,19)(11,25)(14,22)(15,26)(16,30)(20,21)(31,33);(2,3)(4,7,9,21,10,19,8,20)(5,12,14,27,13,28,22,32)(6,16,17,31,18,30,23,33)(11,24,26,34,25,35,15,29);(4,6)(5,11)(7,16)(8,23)(9,17)(10,18)(12,24)(13,25)(14,26)(15,22)(19,30)(20,33)(21,31)(27,34)(28,35)(29,32);(4,5,9,14,10,13,8,22)(6,15,17,11,18,26,23,25)(7,12,21,27,19,28,20,32)(16,29,31,24,30,34,33,35)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,d^c=dg,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10809089, #10809091, #10809097, … |
| maximal normal subgroup of | #10809089, #10809091, #10809097, … |
| maximal quotient of | #10764641, #10764648, #10764655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11566);