Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×#22604421 |
| derived, Sylow | C577 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #14556313 |
| commutator, hypocenter | C577 | C2×C16 |
| Frattini | C4 | C2×#14556313 |
| Fitting | C2×C4×C577 | C4 |
| socle, prime radical | C22×C577 | C8 |
| cosocle | #17987230 | C22 |
| LCS | G ▷ C577 | |
| UCS | C1 ◁ C2×C4 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18464 |
1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22604421, #49148835, #49148837, … |
| maximal normal subgroup of | C4×#22604421, #49148835, #49148837, … |
| maximal quotient of | C4×#22604421, C22⋊#22604421, C4⋊#22604421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 218);