Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C25×D283 |
| unambiguous semidirect product | C283⋊C26 |
| unambiguous semidirect product | (C2×C283)⋊C25 |
| Fitting, socle | C25×C283 ⋊ C2 |
| derived, Sylow | C283 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D283 |
| commutator, cosocle, hypocenter | C283 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C25×C283 | C2 |
| LCS | G ▷ C283 | |
| UCS | C1 ◁ C25 | |
5650 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9056 |
4576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #379×D283, C2×#31826320, #49129537, … |
| maximal normal subgroup of | #379×D283, C2×#31826320, #49129537, … |
| maximal quotient of | C24×C4×D283, C25×Dic283, C23×D4×D283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 1387);