Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×#101 ⋊ C2 |
| Sylow | C7 ⋊ #454 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6445 |
| commutator, cosocle | C2×C4×C7 | C23 |
| Frattini | C2×C4 | C22×D7 |
| Fitting | C7×#101 | C2 |
| socle | C2×C7 | #120 |
| hypercenter | #101 | D7 |
| hypocenter | C7 | #454 |
| LCS | G ▷ C2×C4×C7 ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #101 | |
146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,11,19,9,13,20,12,15)(10,16,21,23,18,22,17,14);(8,10,13,18)(9,14,15,23)(11,16,20,22)(12,21,19,17);(2,3)(4,5)(6,7)(8,9)(10,14)(11,19)(12,20)(13,15)(16,17)(18,23)(21,22)Polycyclic presentation:
2^6,7|b^2=f,c^2=df,d^2=f,c^a=cd,d^a=df,e^a=ef,g^a=g^6,c^b=ce,d^b=df,e^c=ef49 conjugacy classes — view the full character table.
| maximal subgroup of | #11726914, #11726915, #11726921, … |
| maximal normal subgroup of | #11726914, #11726915, #11726921, … |
| maximal quotient of | #11725884, #11725885, #11725890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 287);