Finite Group DatabasebetaFinite Group Databasebeta| order | 18272 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #41×D571 |
| Fitting | #41×C571 ⋊ C2 |
| Sylow | C571 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D571 |
| commutator, socle, cosocle | C2×C571 | C24 |
| Frattini | C2 | C23×D571 |
| Fitting | #41×C571 | C2 |
| hypercenter | #41 | D571 |
| hypocenter | C571 | C2×#41 |
| LCS | G ▷ C2×C571 ▷ C571 | |
| UCS | C1 ◁ C4 ◁ #41 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4568 |
2870 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×D571, #49142281, #131×D571, … |
| maximal normal subgroup of | #104×D571, #49142281, #131×D571, … |
| maximal quotient of | #117×D571, C4×D4×D571, C4×Q8×D571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18272, 187);