Finite Group DatabasebetaFinite Group Databasebeta| order | 18532 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C41×C113 ⋊ C4 |
| Sylow | C113 ⋊ #4223 |
| Sylow | C41 ⋊ Dic113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C41×C113 | C4 |
| prime radical, cosocle | D41×C113 | C2 |
| LCS | G ▷ C41×C113 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4633 |
Polycyclic presentation:
2^2,41,113|a^2=b,c^a=c^32,d^a=d^112,c^b=c^401246 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18532, 10);