Finite Group DatabasebetaFinite Group Databasebeta| order | 26100 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C9×C29 · Schur multiplier (H2) = C2×C5 |
| derived, Sylow | C22 ⋊ C52×C9×C29 |
| Hall | C22×C52×C29 ⋊ C9 |
| Hall | C22×C29 ⋊ C52×C9 |
| Hall | C22×C52 ⋊ C9×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52×C29 | A4 |
| commutator, hypocenter | C22 | C52×C9×C29 |
| Frattini | C3 | C52×A4×C29 |
| Fitting, socle, prime radical | C22×C3×C52×C29 | C3 |
| cosocle | C22×C3 | C3×C52×C29 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C52×C29 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13050 |
8700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26100, 212);