Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89428 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#95 ⋊ C2 |
| Sylow | C7 ⋊ #394 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D7 |
| commutator, socle, cosocle | C23×C7 | C23 |
| Fitting | C7×#95 | C2 |
| prime radical | C22×D28 | C2 |
| hypercenter | #95 | D7 |
| hypocenter | C7 | #394 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #95 | |
238 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(9,11)(12,13,14,15)(16,17)(18,19);(8,9)(10,11)(13,15)(16,17,18,19);(2,3)(4,5)(6,7)(9,11)(17,19)Polycyclic presentation:
2^6,7|b^2=d,c^2=ef,b^a=be,c^a=cd,g^a=g^6,c^b=cf82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726046, #11726047, #11726078, … |
| maximal normal subgroup of | #11726046, #11726047, #11726078, … |
| maximal quotient of | #11726383, #11726384, #11726385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 206);