Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#14556873 |
| derived, Sylow | C293 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D293 |
| commutator, hypocenter | C293 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D293 |
| Fitting | C2×C42×C293 | C2 |
| socle, prime radical | C23×C293 | C2×C4 |
| cosocle | C2×C4×C293 | C23 |
| LCS | G ▷ C293 | |
| UCS | C1 ◁ C2×C42 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18752 |
4736 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49156612, #49156619, #49156621, … |
| maximal normal subgroup of | #49156612, #49156619, #49156621, … |
| maximal quotient of | C2×C8×#14556873, C2×#34035850, M16×#14556873, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 495);