Finite Group DatabasebetaFinite Group Databasebeta| order | 6498 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C192 ⋊ C2×C9 |
| Hall | #15692434 ⋊ C2 |
| Hall | C19×D19 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C192 | C2×C9 |
| LCS | G ▷ C192 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,19^2|b^3=c,d^a=d^18,d^b=d^4,e^b=e^9,d^c=d^7,e^c=e^741 conjugacy classes — view the full character table.
| maximal subgroup of | #20266600⋊C2, C2×#20266604, C5×#20266604, … |
| maximal normal subgroup of | #20266600⋊C2, C2×#20266604, C5×#20266604, … |
| maximal quotient of | #27188767, C2×#20266604, C5×#20266604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6498, 43);