Finite Group DatabasebetaFinite Group Databasebeta| order | 16245 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #15692433⋊C5 |
| Fitting, socle, derived, Sylow | C192 ⋊ C5×C9 |
| Hall | #15692433 ⋊ C5 |
| Hall | C192⋊C5 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C192 | C5×C9 |
| prime radical | #11762245⋊C5 | C3 |
| cosocle | #11762245 | C3×C5 |
| LCS | G ▷ C192 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 95 |
Polycyclic presentation:
3,5,3,19^2|a^3=c,d^a=d^16,e^a=e^16,d^b=d^12e^8,e^b=d^14e^11,d^c=d^11,e^c=e^1153 conjugacy classes — view the full character table.
| maximal subgroup of | #44570497, #20266599⋊C5, C2×#15692433⋊C5 |
| maximal normal subgroup of | #44570497, #20266599⋊C5, C2×#15692433⋊C5 |
| maximal quotient of | C2×#15692433⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16245, 13);