Finite Group DatabasebetaFinite Group Databasebeta| order | 29684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C41×C181 ⋊ C4 |
| Sylow | C181 ⋊ Dic41 |
| Sylow | C41 ⋊ #10624382 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C41×C181 | C4 |
| prime radical, cosocle | C41×D181 | C2 |
| LCS | G ▷ C41×C181 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7421 |
Polycyclic presentation:
2^2,41,181|a^2=b,c^a=c^40,d^a=d^162,d^b=d^1801889 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29684, 11);