Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×D1172 |
| Fitting | C4×Q8×C293 ⋊ C2 |
| Sylow | C293 ⋊ D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D293 |
| commutator, socle, cosocle | C22×C293 | C24 |
| Fitting | C4×Q8×C293 | C2 |
| prime radical | C2×D1172 | C22 |
| hypercenter | C4×Q8 | D293 |
| hypocenter | C293 | D4×Q8 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
2945 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49157886, #49157890, #49157948, … |
| maximal normal subgroup of | #49157886, #49157890, #49157948, … |
| maximal quotient of | Q8×#17989779, C4⋊C4×D1172, Q8×C4⋊Dic293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1216);