Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, Hall | C5×C192 ⋊ C2×D3 |
| derived, Hall | C5×#11762246 ⋊ C22 |
| Hall | #11762246 ⋊ C2×D5 |
| Sylow | C192 ⋊ C2×D15 |
| Sylow | C5 ⋊ #14524212⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×#11762246 | C22 |
| Fitting, socle | C5×C192 | C2×D3 |
| LCS | G ▷ C5×#11762246 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 190 |
Polycyclic presentation:
2^2,3,5,19^2|c^a=c^2,d^a=d^4,e^a=e^11f^6,f^a=e^18f^8,e^b=e^18,f^b=f^18,e^c=e^7f^13,f^c=f^11195 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 122);