Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C271 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D271 |
| commutator | C2×C271 | C22×C4 |
| Frattini | C22 | C22×D271 |
| Fitting | C22×C4×C271 | C2 |
| socle | C22×C271 | C23 |
| hypercenter | C22×C4 | D271 |
| hypocenter | C271 | #117 |
| LCS | G ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,271|a^2=e,c^2=d,b^a=bd,f^a=f^2702180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31773653, #31773654, #31773657, … |
| maximal normal subgroup of | #31773653, #31773654, #31773657, … |
| maximal quotient of | #31773743, C4×C22⋊Dic271, C4×C4⋊Dic271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 105);