Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3121 |
370 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)(4,6,7,10)(5,9,8,11)(13,18)(17,25)(19,26)(24,27);(2,3)(12,14,16,21)(13,17,18,25)(15,23,22,20)(19,27,26,24);(5,8)(9,11)(12,13)(14,17)(15,19)(16,18)(20,24)(21,25)(22,26)(23,27);(4,5)(6,9)(7,8)(10,11)(14,20)(15,22)(17,24)(19,26)(21,23)(25,27)Polycyclic presentation:
2^7,3|c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,f^c=fg,h^c=h^2,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3121, C2×#81353, #11663548, … |
| maximal normal subgroup of | D3×#3121, C2×#81353, #11663548, … |
| maximal quotient of | #10795283, #10798288, #10798307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13929);