Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D7 |
| commutator, socle | C2×C7 | C22×C8 |
| Fitting | C7×#131 | C2 |
| prime radical | C7×#41 | C4 |
| cosocle | C7×C8 | C23 |
| hypercenter | #131 | D7 |
| hypocenter | C7 | #504 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C8 ◁ #131 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,4,6,7,5,3)(10,18)(14,24)(19,30)(20,31)(25,34)(26,35)(32,38)(36,39);(8,10)(9,14)(11,19)(12,20)(13,18)(15,25)(16,26)(17,24)(21,32)(22,30)(23,31)(27,36)(28,34)(29,35)(33,38)(37,39);(2,3)(4,5)(6,7)(8,9,11,15,12,16,21,27,13,17,22,28,23,29,33,37)(10,14,19,25,20,26,32,36,18,24,30,34,31,35,38,39)Polycyclic presentation:
2^6,7|a^2=d,d^2=e,e^2=f,g^a=g^6,c^b=cf100 conjugacy classes — view the full character table.
| maximal subgroup of | #11726876, #11726877, #11728677, … |
| maximal normal subgroup of | #11726876, #11726877, #11728677, … |
| maximal quotient of | #11727635, #11727636, #11727637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 674);