Finite Group DatabasebetaFinite Group Databasebeta| order | 7375 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×5−1+2 |
| unambiguous semidirect product | C25⋊(C5×C59) |
| unambiguous semidirect product | (C25×C59)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C5×C59 | C52 |
| commutator, Frattini | C5 | C52×C59 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C5×C59 ◁ G | |
20 conjugacy classes of subgroups.
1711 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C59×#10597831, C59×#10597832, C59×#10597833, … |
| maximal normal subgroup of | C59×#10597831, C59×#10597832, C59×#10597833, … |
| maximal quotient of | C59×C52⋊C25, C59×C25⋊C25, C5×C59×5−1+2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7375, 4);