Finite Group DatabasebetaFinite Group Databasebeta| order | 5427 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C67 ⋊ #737 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×C67⋊C3 |
| commutator, socle | C3×C67 | C33 |
| Fitting | H(3,𝔽3)×C67 | C3 |
| hypercenter | H(3,𝔽3) | C67⋊C3 |
| hypocenter | C67 | #737 |
| LCS | G ▷ C3×C67 ▷ C67 | |
| UCS | C1 ◁ C3 ◁ H(3,𝔽3) | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,67|c^3=d,b^a=bd,e^c=e^37275 conjugacy classes — view the full character table.
| maximal subgroup of | #30653979, #30653981, #30653982, … |
| maximal normal subgroup of | #30653979, #30653981, #30653982, … |
| maximal quotient of | #30653885, H(3,𝔽3)×C67⋊C9, #30653898, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5427, 46);