Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#17989801 |
| Fitting | C22×D4×C293 ⋊ C2 |
| Sylow | C293 ⋊ C22×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D293 |
| commutator, cosocle | C2×C293 | C25 |
| Frattini | C2 | C24×D293 |
| Fitting | C22×D4×C293 | C2 |
| socle | C23×C293 | C23 |
| hypercenter | C22×D4 | D293 |
| hypocenter | C293 | C22×#41 |
| LCS | G ▷ C2×C293 ▷ C293 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
890 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
2960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49158701, #49158710, #49158722, … |
| maximal normal subgroup of | #49158701, #49158710, #49158722, … |
| maximal quotient of | C22×#22627580, C22×#22627582, C22×#22627584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1375);