Finite Group DatabasebetaFinite Group Databasebeta| order | 7857 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | 3−1+2×C97 ⋊ C3 |
| Sylow | C97 ⋊ #731 |
| subgroup | G/H | |
|---|---|---|
| center | C3 | C32⋊(C97⋊C3) |
| commutator | C32×C97 | C32 |
| Frattini | C32 | C3×C97⋊C3 |
| Fitting | 3−1+2×C97 | C3 |
| socle | C3×C97 | H(3,𝔽3) |
| hypercenter | 3−1+2 | C97⋊C3 |
| hypocenter | C97 | #731 |
| LCS | G ▷ C32×C97 ▷ C3×C97 ▷ C97 | |
| UCS | C1 ◁ C3 ◁ C32 ◁ 3−1+2 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,97|b^3=d,b^a=bc,c^a=cd,e^a=e^61,e^b=e^35369 conjugacy classes — view the full character table.
| maximal subgroup of | #731×C97⋊C3, C3×#21463363, #37555950, … |
| maximal normal subgroup of | #731×C97⋊C3, C3×#21463363, #37555950, … |
| maximal quotient of | #37555765, #37555768, #37555769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7857, 33);