Finite Group DatabasebetaFinite Group Databasebeta| order | 7540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C13×C29 ⋊ C4 |
| Hall | C13×C29 ⋊ AGL(1,𝔽5) |
| Hall | C5×C29 ⋊ #261 |
| Hall | C5×C13 ⋊ #1181 |
| Sylow | C29 ⋊ #63121 |
| Sylow | C13 ⋊ #10596815 |
| Sylow | C5 ⋊ #13094087 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C29 | C4 |
| LCS | G ▷ C5×C13×C29 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,13,29|a^2=b,c^a=c^2,d^a=d^8,e^a=e^12,c^b=c^4,d^b=d^12,e^b=e^28475 conjugacy classes — view the full character table.
| maximal subgroup of | #21419475⋊C3, C3×#21419475, C3⋊#21419475, … |
| maximal normal subgroup of | #21419475⋊C3, C3×#21419475, C5×#21419475 |
| maximal quotient of | C3×#21419475, C3⋊#21419475, #49179375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7540, 27);