Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C7 ⋊ #519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D7 |
| commutator | C2×C7 | C23×C4 |
| Fitting | C22×C7×Q8 | C2 |
| socle, cosocle | C22×C7 | C24 |
| prime radical | C23×C7 | C23 |
| hypercenter | C22×Q8 | D7 |
| hypocenter | C7 | #519 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
266 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,4,6,7,5,3)(13,19)(17,25)(18,27)(24,26);(12,15,16,23)(13,18,19,27)(14,20,21,22)(17,24,25,26);(12,14,16,21)(13,17,19,25)(15,22,23,20)(18,26,27,24);(2,3)(4,5)(6,7)(8,9,10,11)(12,13)(14,17)(15,18)(16,19)(20,24)(21,25)(22,26)(23,27)Polycyclic presentation:
2^6,7|a^2=e,b^2=f,c^2=f,d^a=df,g^a=g^6,c^b=cf94 conjugacy classes — view the full character table.
| maximal subgroup of | #11727426, #11727855, #11727856, … |
| maximal normal subgroup of | #11727426, #11727855, #11727856, … |
| maximal quotient of | #11739589, #11739600, #11739601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1265);