Finite Group DatabasebetaFinite Group Databasebeta| order | 9872 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#14578674 |
| Fitting | C4×C617 ⋊ C4 |
| derived, Sylow | C617 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14578674 |
| commutator, hypocenter | C617 | C42 |
| Frattini | C2 | C2×#14578674 |
| Fitting | C4×C617 | C4 |
| socle | C2×C617 | C2×C4 |
| prime radical, cosocle | C2×D617 | C22 |
| LCS | G ▷ C617 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
632 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14578674, #34089756, #34089766, … |
| maximal normal subgroup of | C8×#14578674, #34089756, #34089766, … |
| maximal quotient of | (C2×#14578674)⋊C4, C8×#14578674, C4×#19096928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9872, 44);