Finite Group DatabasebetaFinite Group Databasebeta| order | 21452 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#10621924 |
| Fitting, socle, Hall | C31×C173 ⋊ C4 |
| derived, Sylow | C173 ⋊ C4×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #10621924 |
| commutator, hypocenter | C173 | C4×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C173 | C4 |
| prime radical | C31×D173 | C2 |
| cosocle | D173 | C2×C31 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C31 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5363 |
1457 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21452, 6);