Finite Group DatabasebetaFinite Group Databasebeta| order | 25116 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×#10587717⋊C2 |
| unambiguous semidirect product | #10587717⋊(C2×C23) |
| unambiguous semidirect product | #10587721⋊(C2×C23) |
| unambiguous semidirect product | #10587723⋊(C2×C23) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #10587717⋊C2 |
| commutator, cosocle, hypocenter | C7×C13 | C22×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C23 | C22×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C23 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2093 |
552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25116, 64);