Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89314 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C7 ⋊ SD64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6400 |
| commutator, cosocle | C7×C16 | C22 |
| Frattini | C16 | C2×D7 |
| Fitting, prime radical | C7×D16 | C2 |
| socle | C2×C7 | D16 |
| hypercenter | D16 | D7 |
| hypocenter | C7 | SD64 |
| LCS | G ▷ C7×C16 ▷ C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D16 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2,4,6,7,5,3)(9,14)(10,19)(11,20)(12,24)(15,16)(17,35)(18,29)(21,38)(22,30)(23,27)(25,33)(26,28)(31,39)(32,34)(36,37);(2,3)(4,5)(6,7)(8,9,13,18)(10,14,22,29)(11,23,25,39)(12,26,24,17)(15,30,32,19)(16,33,34,20)(21,35,36,28)(27,38,31,37)Polycyclic presentation:
2^6,7|a^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^6,c^b=cd,d^b=de,e^b=ef52 conjugacy classes — view the full character table.
| maximal subgroup of | #11727130, #11727131, D7×SD64, … |
| maximal normal subgroup of | #11727130, #11727131, D7×SD64, … |
| maximal quotient of | #11725382, #11725384, #11725630, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 77);