Finite Group DatabasebetaFinite Group Databasebeta| order | 20972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C107⋊#5997 |
| Fitting, socle, derived, Hall | C72×C107 ⋊ C4 |
| Sylow | C107 ⋊ #5997 |
| Sylow | C72 ⋊ Dic107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C107 | C4 |
| prime radical, cosocle | C7⋊D7×C107 | C2 |
| LCS | G ▷ C72×C107 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1498 |
Polycyclic presentation:
2^2,7^2,107|a^2=b,c^a=c^4d^6,d^a=c^3d^3,e^a=e^106,c^b=c^6,d^b=d^61394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20972, 18);