Finite Group DatabasebetaFinite Group Databasebeta| order | 4401 |
| isoclinism | isoclinic class of C163⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C32×C163⋊C3 |
| unambiguous semidirect product | C163⋊C33 |
| unambiguous semidirect product | (C3×C163)⋊C32 |
| Fitting, socle | C32×C163 ⋊ C3 |
| derived, Sylow | C163 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C163⋊C3 |
| commutator, cosocle, hypocenter | C163 | C33 |
| Frattini | C1 | G |
| Fitting, socle | C32×C163 | C3 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C32 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1467 |
513 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27210102, #27210112, #27210114, … |
| maximal normal subgroup of | #27210102, #27210112, #27210114, … |
| maximal quotient of | C3×C9×C163⋊C3, C32×#13091812, H(3,𝔽3)×C163⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4401, 13);