Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C8×Dic283 |
| derived, Sylow | C283 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D283 |
| commutator, hypocenter | C283 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D283 |
| Fitting | C22×C8×C283 | C2 |
| socle, prime radical | C23×C283 | C2×C4 |
| cosocle | C2×C4×C283 | C23 |
| LCS | G ▷ C283 | |
| UCS | C1 ◁ C22×C8 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18112 |
4576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49119338, #49119342, C4×C8×Dic283, … |
| maximal normal subgroup of | #49119338, #49119342, C4×C8×Dic283, … |
| maximal quotient of | C2×C8×C283⋊C8, C2×#31826187, C8×#17985376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 494);