Finite Group DatabasebetaFinite Group Databasebeta| order | 25270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#16813380 |
| Fitting, socle, Hall | C7×C192 ⋊ D5 |
| derived, Hall | C192⋊C5 ⋊ C2×C7 |
| Hall | C7×C192⋊C5 ⋊ C2 |
| Sylow | C192 ⋊ C7×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #16813380 |
| commutator, cosocle, hypocenter | C192⋊C5 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C192 | D5 |
| LCS | G ▷ C192⋊C5 | |
| UCS | C1 ◁ C7 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 665 |
469 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25270, 10);