Finite Group DatabasebetaFinite Group Databasebeta| order | 7900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C79⋊#1035 |
| Fitting, derived, Hall | C25×C79 ⋊ C4 |
| Sylow | C79 ⋊ #1035 |
| Sylow | C25 ⋊ Dic79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C79 | C4 |
| Frattini | C5 | C79⋊AGL(1,𝔽5) |
| socle | C5×C79 | AGL(1,𝔽5) |
| LCS | G ▷ C25×C79 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,79,5|a^2=b,c^5=e,c^a=c^2e,d^a=d^78,e^a=e^2,c^b=c^4e^4,e^b=e^4556 conjugacy classes — view the full character table.
| maximal subgroup of | (C79⋊C3)⋊#1035, C3×C79⋊#1035, C3⋊(C79⋊#1035) |
| maximal normal subgroup of | (C79⋊C3)⋊#1035, C3×C79⋊#1035 |
| maximal quotient of | C3×C79⋊#1035, C3⋊(C79⋊#1035) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7900, 7);