Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#125 ⋊ C2 |
| Sylow | C7 ⋊ #562 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D7 |
| commutator, socle, cosocle | C22×C7 | C24 |
| Fitting | C7×#125 | C2 |
| hypercenter | #125 | D7 |
| hypocenter | C7 | #562 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #125 | |
220 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,4,6,7,5,3)(8,11,12,10)(9,13,14,15)(16,18,19,22)(17,21,20,23);(8,10,12,11)(9,13,14,15)(16,17)(18,21)(19,20)(22,23);(8,9,12,14)(10,13,11,15)(17,20)(18,22);(2,3)(4,5)(6,7)(10,11)(13,15)(17,20)(21,23)Polycyclic presentation:
2^6,7|b^2=e,c^2=e,d^2=f,c^a=cf,d^a=de,g^a=g^6,c^b=cef,d^b=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11726124, #11726127, #11726128, … |
| maximal normal subgroup of | #11726124, #11726127, #11726128, … |
| maximal quotient of | #11731643, #11731646, #11731664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1153);