Finite Group DatabasebetaFinite Group Databasebeta| order | 27716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C41 ⋊ C4 |
| Sylow | C132 ⋊ Dic41 |
| Sylow | C41 ⋊ #10621728 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132×C41 | C4 |
| prime radical, cosocle | C41×C13⋊D13 | C2 |
| LCS | G ▷ C132×C41 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6929 |
Polycyclic presentation:
2^2,13^2,41|a^2=b,c^a=c^5,d^a=d^5,e^a=e^40,c^b=c^12,d^b=d^121766 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27716, 45);