Finite Group DatabasebetaFinite Group Databasebeta| order | 441 |
| isoclinism | isoclinic class of #3862 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C7 |
No aliases for this group.
| derived, Sylow | C72 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #3862 |
| commutator, hypocenter | C72 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C72 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 63 |
A minimal faithful permutation representation — 2 generators on 23 points:
(2,3,4)(5,7,6)(9,10,11)(12,14,13)(15,16,18,17,19,21,20,22,23);(1,2,4,6,3,5,7)(8,9,10,12,11,13,14)Polycyclic presentation:
3^2,7^2|a^3=b,c^a=c^4,d^a=d^257 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(441, 7);