Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3178 |
350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 27 points:
(2,3)(4,6,7,10)(5,9,8,11)(13,18)(17,21)(19,25)(24,26);(1,2,3)(12,14,15,20,16,22,23,27)(13,17,19,24,18,21,25,26);(5,8)(9,11)(12,13)(14,21)(15,19)(16,18)(17,22)(20,26)(23,25)(24,27);(4,5)(6,9)(7,8)(10,11)(14,20)(15,23)(17,24)(19,25)(21,26)(22,27)Polycyclic presentation:
2^7,3|c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=dg,h^d=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3178, C2×#80788, #11665080, … |
| maximal normal subgroup of | D3×#3178, C2×#80788, #11665080, … |
| maximal quotient of | #10795761, #10799470, #10799490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13364);