Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of D112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #358 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,4,6,7,5,3)(8,10,11,9)(12,13,18,27,16,20,14,17,15,19,21,26,22,24,23,25);(2,3)(4,5)(6,7)(8,9,11,10)(13,17)(14,21)(16,22)(18,23)(19,25)(20,27)(24,26)Polycyclic presentation:
2^6,7|a^2=df,b^2=cde,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^6118 conjugacy classes — view the full character table.
| maximal subgroup of | #11726813, C4×#6374, C4×Dic56, … |
| maximal normal subgroup of | #11726813, C4×#6374, C4×Dic56, … |
| maximal quotient of | #11725311, #11725334, #11725367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 60);