Finite Group DatabasebetaFinite Group Databasebeta| order | 8672 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #41×D271 |
| Fitting | #41×C271 ⋊ C2 |
| Sylow | C271 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D271 |
| commutator, socle | C2×C271 | C24 |
| Frattini | C2 | C23×D271 |
| Fitting | #41×C271 | C2 |
| hypercenter | #41 | D271 |
| hypocenter | C271 | C2×#41 |
| LCS | G ▷ C2×C271 ▷ C271 | |
| UCS | C1 ◁ C4 ◁ #41 | |
164 conjugacy classes of subgroups.
1370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×D271, #31773912, #131×D271, … |
| maximal normal subgroup of | #104×D271, #31773912, #131×D271, … |
| maximal quotient of | #117×D271, C4×D4×D271, C4×Q8×D271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8672, 187);