Finite Group DatabasebetaFinite Group Databasebeta| order | 26574 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C43×C103 ⋊ C2×C3 |
| Hall | #27210791 ⋊ C2 |
| Hall | C43×D103 ⋊ C3 |
| Hall | D103 ⋊ C43⋊C3 |
| Sylow | C103 ⋊ C2×C43⋊C3 |
| Sylow | C43 ⋊ D103⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C103 | C2×C3 |
| LCS | G ▷ C43×C103 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4429 |
Polycyclic presentation:
2,3,43,103|d^a=d^102,c^b=c^36,d^b=d^46765 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26574, 16);