Finite Group DatabasebetaFinite Group Databasebeta| order | 33620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C41 |
No aliases for this group.
| Fitting, socle, Sylow | C412 ⋊ Dic5 |
| derived, Hall | #22554263 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | #22554263 | C4 |
| Fitting, socle | C412 | Dic5 |
| prime radical, cosocle | #30681146 | C2 |
| LCS | G ▷ #22554263 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 82 |
Polycyclic presentation:
2^2,5,41^2|a^2=b,c^a=c^4,d^a=d^23e^32,e^a=d^27e^18,d^b=d^40,e^b=e^40,d^c=d^16e^26,e^c=e^1892 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33620, 43);