Finite Group DatabasebetaFinite Group Databasebeta| order | 7375 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 116000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C5 |
| abelian | C5×C25×C59 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C5 | C52×C59 |
| socle | C52×C59 | C5 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
28 conjugacy classes of subgroups.
7375 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C252×C59, C59×C52⋊C25, C59×C25⋊C25, … |
| maximal normal subgroup of | C252×C59, C59×C52⋊C25, C59×C25⋊C25, … |
| maximal quotient of | C252×C59, C59×C52⋊C25, C59×C25⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7375, 2);