Finite Group DatabasebetaFinite Group Databasebeta| order | 25308 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C19×C37 ⋊ C4×C9 |
| Hall | #20263539 ⋊ C4 |
| Hall | C19×#3866 ⋊ C9 |
| Hall | #3866 ⋊ #4294 |
| Sylow | C37 ⋊ C4×#4294 |
| Sylow | C19 ⋊ #13050613 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #22554665 |
| commutator, hypocenter | C19×C37 | C4×C9 |
| Fitting, socle | C3×C19×C37 | C3×C4 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,19,37,3|a^2=c,b^3=f,e^a=e^31,d^b=d^7,e^b=e^10,e^c=e^36279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25308, 34);