Finite Group DatabasebetaFinite Group Databasebeta| order | 7100 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×#1035 |
| Fitting, Hall | C25×C71 ⋊ C4 |
| derived, Sylow | C25 ⋊ C4×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | #1035 |
| commutator, hypocenter | C25 | C4×C71 |
| Frattini | C5 | AGL(1,𝔽5)×C71 |
| Fitting | C25×C71 | C4 |
| socle | C5×C71 | AGL(1,𝔽5) |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C71 | |
18 conjugacy classes of subgroups.
710 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C71×#1035, C71×C3⋊#1035 |
| maximal normal subgroup of | C3×C71×#1035 |
| maximal quotient of | C3×C71×#1035, C71×C3⋊#1035 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7100, 10);