Finite Group DatabasebetaFinite Group Databasebeta| order | 4107 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C372 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C372 | C3 |
| LCS | G ▷ C372 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1369 |
Polycyclic presentation:
3,37^2|b^a=b^26,c^a=c^26459 conjugacy classes — view the full character table.
| maximal subgroup of | C37⋊C32, #27134467, #27134468, … |
| maximal normal subgroup of | C37⋊C32, #27134467, #27134468, … |
| maximal quotient of | #27134460, C3×#16861551, C22⋊#16861551, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4107, 4);