Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #544 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D7 |
| commutator, socle, cosocle | C22×C7 | C24 |
| Fitting | C2×C7×C4⋊C4 | C2 |
| prime radical | C23×C7 | C23 |
| hypercenter | C2×C4⋊C4 | D7 |
| hypocenter | C7 | #544 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C2×C4⋊C4 | |
206 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)(10,14)(12,15)(16,18,19,23)(17,20,21,22);(9,13)(12,15);(8,10,11,14)(9,12,13,15);(2,3)(4,5)(6,7)(8,9)(10,12)(11,13)(14,15)(16,17,19,21)(18,22,23,20)Polycyclic presentation:
2^6,7|a^2=e,b^2=f,d^2=e,c^a=cf,d^a=de,g^a=g^6,d^b=df82 conjugacy classes — view the full character table.
| maximal subgroup of | #11725892, #11725893, #11725894, … |
| maximal normal subgroup of | #11725892, #11725893, #11725894, … |
| maximal quotient of | #11730779, #11730795, #11730805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 953);