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 | C7×#117 | C2 |
| socle, cosocle | C22×C7 | C24 |
| prime radical | C23×C7 | C23 |
| hypercenter | #117 | D7 |
| hypocenter | C7 | #519 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #117 | |
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)(8,9,10,11)(14,21)(17,25)(20,27)(24,26);(12,15,16,23)(13,18,19,22)(14,20,21,27)(17,24,25,26);(12,14)(13,17)(15,20)(16,21)(18,24)(19,25)(22,26)(23,27);(2,3)(4,5)(6,7)(12,13,16,19)(14,17,21,25)(15,22,23,18)(20,26,27,24)Polycyclic presentation:
2^6,7|a^2=f,c^2=f,d^2=e,c^a=cf,g^a=g^6,d^b=df94 conjugacy classes — view the full character table.
| maximal subgroup of | #11726461, #11726462, #11726518, … |
| maximal normal subgroup of | #11726461, #11726462, #11726518, … |
| maximal quotient of | #11730828, #11730831, #11730833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 969);