Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C271 ⋊ C2 |
| Sylow | C271 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D271 |
| commutator, socle | C2×C271 | C24 |
| Fitting | #41×C271 | C2 |
| hypercenter | #41 | D271 |
| hypocenter | C271 | H(5,𝔽2) |
| LCS | G ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,271|b^a=be,d^a=de,c^b=ce,f^c=f^270,f^d=f^2701367 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31774063, #31774066, #31774073, … |
| maximal normal subgroup of | #31774063, #31774066, #31774073, … |
| maximal quotient of | #31774369, #31774371, #31774377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 192);