Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C7×SD16 ⋊ C2 |
| Sylow | C7 ⋊ #495 |
130 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,7,5,3)(9,11)(12,14,16,22)(13,18,17,20)(15,24,23,21)(19,26,25,27);(9,11)(13,17)(14,21)(15,23)(18,26)(20,27)(22,24);(2,3)(4,5)(6,7)(8,9,10,11)(12,13)(14,20)(15,19)(16,17)(18,22)(21,26)(23,25)(24,27)Polycyclic presentation:
2^6,7|a^2=e,c^2=f,d^2=f,b^a=bef,c^a=cef,g^a=g^6,c^b=cd,d^b=df,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | #11737083, #11737084, #11737108, … |
| maximal normal subgroup of | #11737083, #11737084, #11737108, … |
| maximal quotient of | #11727912, #11727936, #11727944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 702);