Finite Group DatabasebetaFinite Group Databasebeta| order | 19025 |
| automorphism | ? |
| homology | Abelianization (H1) = C52 · Schur multiplier (H2) = C5 |
| direct product | C5×C761⋊C5 |
| unambiguous semidirect product | C761⋊C52 |
| unambiguous semidirect product | (C5×C761)⋊C5 |
| Fitting, socle | C5×C761 ⋊ C5 |
| derived, Sylow | C761 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C761⋊C5 |
| commutator, cosocle, hypocenter | C761 | C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C761 | C5 |
| LCS | G ▷ C761 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3805 |
785 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D761⋊C5, C5⋊(D761⋊C5), D5×C761⋊C5, … |
| maximal normal subgroup of | C5×D761⋊C5, C5⋊(D761⋊C5), D5×C761⋊C5, … |
| maximal quotient of | C2×C5×C761⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19025, 3);