Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D271)⋊C8 |
| Fitting | C2×C8×C271 ⋊ C2 |
| Sylow | C271 ⋊ C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D271 |
| commutator | C2×C271 | C2×C8 |
| Fitting | C2×C8×C271 | C2 |
| socle | C22×C271 | C2×C4 |
| hypercenter | C2×C8 | D271 |
| hypocenter | C271 | C22⋊C8 |
| LCS | G ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,271|a^2=d,d^2=e,b^a=bc,f^b=f^2702180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C8×D271, C2×(C2×D271)⋊C8, #31773859, … |
| maximal normal subgroup of | C22⋊C8×D271, C2×(C2×D271)⋊C8, #31773859, … |
| maximal quotient of | #31773620, #31773622, #31773624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 58);