Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C7×M16 ⋊ C2 |
| Sylow | C7 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D7 |
| commutator, socle | C2×C7 | C23×C4 |
| Fitting | C2×C7×M16 | C2 |
| prime radical | C2×#1157 | C2 |
| cosocle | C4×C7 | C24 |
| hypercenter | C2×M16 | D7 |
| hypocenter | C7 | #568 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,4,6,7,5,3)(8,10,11,17,12,16,18,22)(9,14,15,21,13,19,20,23);(9,13)(14,19)(15,20)(21,23);(10,16)(14,19)(17,22)(21,23);(2,3)(4,5)(6,7)(8,9)(10,14)(11,15)(12,13)(16,19)(17,21)(18,20)(22,23)Polycyclic presentation:
2^6,7|d^2=e,e^2=f,c^a=cf,g^a=g^6,d^b=df94 conjugacy classes — view the full character table.
| maximal subgroup of | #11726466, #11726467, #11726479, … |
| maximal normal subgroup of | #11726466, #11726467, #11726479, … |
| maximal quotient of | #11735925, #11735926, #11735927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1198);