Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3348 |
348 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,3)(6,11)(9,10)(12,15,16,17)(13,19,20,24)(14,23,22,25)(18,27,26,21);(4,7,8,5)(6,10,11,9)(12,14)(13,18)(15,23)(16,22)(17,25)(19,27)(20,26)(21,24);(4,6)(5,9)(7,10)(8,11)(14,22)(18,26)(21,27)(23,25);(2,3)(4,5,8,7)(6,10,11,9)(12,13,16,20)(14,21,22,27)(15,19,17,24)(18,25,26,23)Polycyclic presentation:
2^7,3|a^2=e,c^2=eg,d^2=g,f^2=g,b^a=beg,c^a=cf,f^a=fg,h^a=h^2,c^b=cg,d^b=deg,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3348, C2×#83649, #11673840, … |
| maximal normal subgroup of | D3×#3348, C2×#83649, #11673840, … |
| maximal quotient of | #10811490, #10811544, #10812902, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16225);