Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#22627621 |
| Fitting | C2×C42×C293 ⋊ C2 |
| Sylow | C293 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D293 |
| commutator, cosocle | C22×C293 | C24 |
| Frattini | C22 | C23×D293 |
| Fitting | C2×C42×C293 | C2 |
| socle | C23×C293 | C23 |
| hypercenter | C2×C42 | D293 |
| hypocenter | C293 | C2×#127 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
4700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#34035872, #49157452, #49157454, … |
| maximal normal subgroup of | C2×#34035872, #49157452, #49157454, … |
| maximal quotient of | C2×#34035999, C2×#34036031, C4×#22627621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1089);