Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #427 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,7,5,3)(12,15,16,23,17,24,14,21)(13,19,18,22,20,26,25,27);(12,14,17,16)(13,18,20,25)(15,21,24,23)(19,22,26,27);(2,3)(4,5)(6,7)(8,9,10,11)(12,13)(14,18)(15,22)(16,25)(17,20)(19,23)(21,26)(24,27)Polycyclic presentation:
2^6,7|a^2=d,b^2=f,c^2=e,e^2=f,c^a=ce,e^a=ef,g^a=g^6124 conjugacy classes — view the full character table.
| maximal subgroup of | #11725527, #11725531, #11725535, … |
| maximal normal subgroup of | #11725527, #11725531, #11725535, … |
| maximal quotient of | #11727483, #11727486, C4×#6391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 640);