Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3201 |
390 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)(5,9)(8,10)(13,18)(17,25)(19,26)(24,27);(2,3)(6,11)(8,10)(12,14,16,21)(13,17,18,25)(15,23,22,20)(19,27,26,24);(4,6)(5,8)(7,11)(9,10)(12,13)(14,17)(15,19)(16,18)(20,24)(21,25)(22,26)(23,27);(4,5)(6,10)(7,9)(8,11)(14,20)(15,22)(17,24)(19,26)(21,23)(25,27)Polycyclic presentation:
2^7,3|c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3201, C2×#83428, #11665908, … |
| maximal normal subgroup of | D3×#3201, C2×#83428, #11665908, … |
| maximal quotient of | #10804289, #10804304, #10805483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16004);