Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C22×#17989805 |
| derived, Sylow | C293 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #11924078 |
| commutator, hypocenter | C293 | C22×C16 |
| Frattini | C4 | C22×#11924078 |
| Fitting | C22×C4×C293 | C4 |
| socle, prime radical | C23×C293 | C8 |
| cosocle | #14556873 | C23 |
| LCS | G ▷ C293 | |
| UCS | C1 ◁ C22×C4 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18752 |
1232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49173823, #49173824, #49173839, … |
| maximal normal subgroup of | #49173823, #49173824, #49173839, … |
| maximal quotient of | C2×C4×#17989805, C2×C22⋊#17989805, C2×C4⋊#17989805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1602);