Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #416 |
158 conjugacy classes of subgroups.
| 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)(13,18)(15,23)(17,24)(19,20)(21,27)(25,26);(12,14,16,22)(13,17,20,26)(15,21,23,27)(18,24,19,25);(2,3)(4,5)(6,7)(8,9,10,11)(12,13)(14,17)(15,18)(16,20)(19,23)(21,24)(22,26)(25,27)Polycyclic presentation:
2^6,7|a^2=e,b^2=f,d^2=f,c^a=cd,d^a=df,g^a=g^6,d^c=df88 conjugacy classes — view the full character table.
| maximal subgroup of | #11727750, #11727751, #11727752, … |
| maximal normal subgroup of | #11727750, #11727751, #11727752, … |
| maximal quotient of | #11729329, #11729334, #11729359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 767);