Finite Group DatabasebetaFinite Group Databasebeta| order | 7900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C79⋊#1043 |
| Fitting, socle, derived, Hall | C52×C79 ⋊ C4 |
| Sylow | C79 ⋊ #1043 |
| Sylow | C52 ⋊ Dic79 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C79 | C4 |
| LCS | G ▷ C52×C79 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,79|a^2=b,c^a=c^2,d^a=d^2,e^a=e^78,c^b=c^4,d^b=d^4556 conjugacy classes — view the full character table.
| maximal subgroup of | #37557196, #37557198, (C79⋊C3)⋊#1043, … |
| maximal normal subgroup of | #37557196, #37557198, (C79⋊C3)⋊#1043, … |
| maximal quotient of | C3×C79⋊#1043, C3⋊(C79⋊#1043) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7900, 23);