Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C32 · Schur multiplier (H2) = C8 |
| direct product | C8×#14556681 |
| derived, Sylow | C73 ⋊ C8×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | #10596842 |
| commutator, hypocenter | C73 | C8×C32 |
| Frattini | C42 | C2×#10596842 |
| Fitting | C4×C8×C73 | C8 |
| socle, prime radical | C22×C73 | C4×C16 |
| cosocle | C4×#11924031 | C22 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C4×C8 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18688 |
544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116576);