Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #41×D317 |
| Fitting | #41×C317 ⋊ C2 |
| Sylow | C317 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D317 |
| commutator, socle, cosocle | C2×C317 | C24 |
| Frattini | C2 | C23×D317 |
| Fitting | #41×C317 | C2 |
| hypercenter | #41 | D317 |
| hypocenter | C317 | C2×#41 |
| LCS | G ▷ C2×C317 ▷ C317 | |
| UCS | C1 ◁ C4 ◁ #41 | |
164 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×D317, #35203238, #131×D317, … |
| maximal normal subgroup of | #104×D317, #35203238, #131×D317, … |
| maximal quotient of | #117×D317, C4×D4×D317, C4×Q8×D317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 187);