Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,7,5,3)(8,10,11,9)(14,20)(15,23)(17,24)(18,27)(21,22)(25,26);(12,14,16,22)(13,17,19,26)(15,20,23,21)(18,24,27,25);(2,3)(4,5)(6,7)(8,9,11,10)(12,13,16,19)(14,17,22,26)(15,18,23,27)(20,24,21,25)Polycyclic presentation:
2^6,7|a^2=e,b^2=f,c^2=ef,d^2=f,g^a=g^6,c^b=cd,d^b=df,d^c=df70 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89562, #11736219, #11736251, … |
| maximal normal subgroup of | C2×#89562, #11736219, #11736251, … |
| maximal quotient of | #11725967, #11725972, #11725973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 324);