Finite Group DatabasebetaFinite Group Databasebeta| order | 8125 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1392768000000 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C56 |
| abelian | C54×C13 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2240 conjugacy classes of subgroups.
8125 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C54×C13, C3×C54×C13 |
| maximal normal subgroup of | C2×C54×C13, C3×C54×C13 |
| maximal quotient of | C2×C54×C13, C3×C54×C13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8125, 15);