Finite Group DatabasebetaFinite Group Databasebeta| order | 441 |
| isoclinism | isoclinic class of #3861 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C72 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #3861 |
| commutator, hypocenter | C72 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C72 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C3 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 441 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,3,5,7,6,8,9)(11,12,13)(14,16,15)(18,19,20)(21,23,22);(17,18,19,21,20,22,23);(10,11,12,14,13,15,16)Polycyclic presentation:
3^2,7^2|a^3=b,c^a=c^2,d^a=d^257 conjugacy classes — view the full character table.
| maximal subgroup of | #11725076, #11725077, C2×#89204, … |
| maximal normal subgroup of | #11725076, #11725077, C2×#89204, … |
| maximal quotient of | C2×#89204, #13050493, C3×#89204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(441, 6);