Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3376 |
346 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)(4,6,7,11)(5,9,8,10)(14,22)(17,21)(23,27)(25,26);(13,18)(14,22)(16,24)(17,25)(19,20)(21,26);(2,3)(4,5,7,8)(6,10,11,9)(12,14,15,22)(13,17,19,21)(16,23,24,27)(18,26,20,25);(5,8)(9,10)(12,13,15,19)(14,21,22,17)(16,18,24,20)(23,25,27,26)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^2,f^c=fg,h^d=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3376, C2×#80523, #11674993, … |
| maximal normal subgroup of | D3×#3376, C2×#80523, #11674993, … |
| maximal quotient of | #10811855, #10812061, #10814184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13099);