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 ⋊ #541 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D7 |
| commutator, socle, cosocle | C22×C7 | C24 |
| Fitting | C7×#125 | C2 |
| prime radical | C22×D7 | C23 |
| hypercenter | #125 | D7 |
| hypocenter | C7 | #541 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ #125 | |
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)(8,10,11,15)(9,13,12,14)(17,23)(19,28)(21,30)(24,27);(8,9,11,12)(10,14,15,13)(16,19)(17,22)(18,24)(20,28)(21,29)(23,26)(25,27)(30,31);(16,18,20,25)(17,21,23,30)(19,27,28,24)(22,31,26,29);(2,3)(4,5)(6,7)(9,12)(13,14)(16,17)(18,21)(19,26)(20,23)(22,28)(24,31)(25,30)(27,29)Polycyclic presentation:
2^6,7|b^2=e,c^2=ef,d^2=ef,c^a=cf,d^a=de,g^a=g^6,c^b=ce,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | #11738590, #11738592, #11738628, … |
| maximal normal subgroup of | #11738590, #11738592, #11738628, … |
| maximal quotient of | #11731597, #11731618, #11731638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1150);