Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×D7 |
| commutator | C2×C7 | C4×C8 |
| Fitting | C2×C7×C16 | C2 |
| socle, prime radical | C22×C7 | C2×C8 |
| cosocle | C2×C7×C8 | C22 |
| hypercenter | C2×C16 | D7 |
| hypocenter | C7 | #346 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C16 | |
54 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)(12,13,14,18,15,19,20,25,16,17,21,23,22,24,26,27);(2,3)(4,5)(6,7)(8,9,10,11)(13,17)(18,23)(19,24)(25,27)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^6136 conjugacy classes — view the full character table.
| maximal subgroup of | #11725406, #11726802, C4×#6372, … |
| maximal normal subgroup of | #11725406, #11726802, C4×#6372, … |
| maximal quotient of | #11725304, #11725305, #11725406, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 59);