Finite Group DatabasebetaFinite Group Databasebeta| order | 25620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×#14579420 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #14579420 |
| commutator, cosocle, hypocenter | C7×C61 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C7×C61 | C2×C3 |
| LCS | G ▷ C7×C61 | |
| UCS | C1 ◁ C2×C5 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4270 |
800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25620, 209);