Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | M16×D317 |
| Fitting | M16×C317 ⋊ C2 |
| Sylow | C317 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D317 |
| commutator, socle | C2×C317 | C22×C4 |
| Fitting | M16×C317 | C2 |
| prime radical | C22×D317 | C4 |
| cosocle | C4×C317 | C23 |
| hypercenter | M16 | D317 |
| hypocenter | C317 | C2×M16 |
| LCS | G ▷ C2×C317 ▷ C317 | |
| UCS | C1 ◁ C4 ◁ M16 | |
68 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×D317, #101×D317, #35203204, … |
| maximal normal subgroup of | #100×D317, #101×D317, #35203204, … |
| maximal quotient of | #97×D317, M16×Dic317, #35203175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 149);