Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C7×Q8 ⋊ C2 |
| Sylow | C7 ⋊ #520 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D7 |
| commutator | C2×C7 | C23×C4 |
| Fitting | C4×C7×Q8 | C2 |
| socle, cosocle | C22×C7 | C24 |
| prime radical | C2×#1161 | C2 |
| hypercenter | C4×Q8 | D7 |
| hypocenter | C7 | #520 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,4,6,7,5,3)(8,10,11,9)(12,14,15,18)(13,17,16,19);(8,9,11,10)(13,16)(17,19);(12,13,15,16)(14,17,18,19);(2,3)(4,5)(6,7)(14,18)(17,19)Polycyclic presentation:
2^6,7|b^2=e,c^2=ef,d^2=f,d^a=de,g^a=g^6,c^b=ce94 conjugacy classes — view the full character table.
| maximal subgroup of | #11737092, #11737095, #11737142, … |
| maximal normal subgroup of | #11737092, #11737095, #11737142, … |
| maximal quotient of | #11731071, #11731074, #11731078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1027);