Finite Group DatabasebetaFinite Group Databasebeta| order | 23780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C29×C41 ⋊ C4 |
| Hall | C29×C41 ⋊ AGL(1,𝔽5) |
| Hall | C5×C41 ⋊ #1181 |
| Hall | C5×C29 ⋊ #4223 |
| Sylow | C41 ⋊ #10596815 |
| Sylow | C29 ⋊ #11717962 |
| Sylow | C5 ⋊ #18011700 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C29×C41 | C4 |
| prime radical, cosocle | D5945 | C2 |
| LCS | G ▷ C5×C29×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5945 |
Polycyclic presentation:
2^2,5,29,41|a^2=b,c^a=c^2,d^a=d^12,e^a=e^9,c^b=c^4,d^b=d^28,e^b=e^401490 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23780, 42);