Finite Group DatabasebetaFinite Group Databasebeta| order | 30740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C29×C53 ⋊ C4 |
| Hall | C29×C53 ⋊ AGL(1,𝔽5) |
| Hall | C5×C53 ⋊ #1181 |
| Hall | C5×C29 ⋊ #6157 |
| Sylow | C53 ⋊ #10596814 |
| Sylow | C29 ⋊ #11761505 |
| Sylow | C5 ⋊ #20259617 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C29×C53 | C4 |
| prime radical, cosocle | D7685 | C2 |
| LCS | G ▷ C5×C29×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7685 |
Polycyclic presentation:
2^2,5,29,53|a^2=b,c^a=c^2,d^a=d^17,e^a=e^30,c^b=c^4,d^b=d^28,e^b=e^521925 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30740, 22);