Finite Group DatabasebetaFinite Group Databasebeta| order | 27716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C41 ⋊ C4 |
| Sylow | C132 ⋊ #4223 |
| Sylow | C41 ⋊ #10621725 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132×C41 | C4 |
| prime radical, cosocle | C132×D41 | 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^12,d^a=d^12,e^a=e^32,e^b=e^401862 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27716, 37);