Finite Group DatabasebetaFinite Group Databasebeta| order | 3100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | C5⋊D5×D31 |
| unambiguous semidirect product | (C5×D31)⋊D5 |
| Fitting, socle, derived, Hall | C52×C31 ⋊ C22 |
| Sylow | C31 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C31 | C22 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 775 |
238 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C5⋊D5×D31, D31×C5⋊D35, C5⋊D5×D217, … |
| maximal normal subgroup of | C7×C5⋊D5×D31, C11×C5⋊D5×D31 |
| maximal quotient of | C7×C5⋊D5×D31, D31×C5⋊D35, C5⋊D5×D217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3100, 43);