Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#22627593 |
| Fitting | C25×C293 ⋊ C2 |
| Sylow | C293 ⋊ C2×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D293 |
| commutator, cosocle | C22×C293 | C24 |
| Frattini | C22 | C23×D293 |
| Fitting | C25×C293 | C2 |
| socle | C23×C293 | C23 |
| hypercenter | C25 | D293 |
| hypocenter | C293 | C2×#120 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C23 ◁ C25 | |
662 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
4700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49159190, #49159236, #49159238, … |
| maximal normal subgroup of | #49159190, #49159236, #49159238, … |
| maximal quotient of | C2×#34035985, C2×#34036002, C2×#34036008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1035);