Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #541 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D7 |
| commutator, socle, cosocle | C22×C7 | C24 |
| Fitting | C7×#117 | C2 |
| prime radical | C23×C7 | C23 |
| hypercenter | #117 | D7 |
| hypocenter | C7 | #541 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #117 | |
192 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,4,6,7,5,3)(9,13)(12,15)(16,19,20,27)(17,22,23,29)(18,25,26,31)(21,28,24,30);(8,10,11,14)(9,12,13,15)(19,27)(22,29)(25,31)(28,30);(16,18,20,26)(17,21,23,24)(19,25,27,31)(22,28,29,30);(2,3)(4,5)(6,7)(8,9)(10,12)(11,13)(14,15)(16,17,20,23)(18,24,26,21)(19,22,27,29)(25,30,31,28)Polycyclic presentation:
2^6,7|a^2=f,b^2=f,c^2=e,d^2=f,b^a=bf,d^a=de,g^a=g^6,d^c=df82 conjugacy classes — view the full character table.
| maximal subgroup of | #11736012, #11736015, #11736022, … |
| maximal normal subgroup of | #11736012, #11736015, #11736022, … |
| maximal quotient of | #11730831, #11730833, #11730835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 971);