Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| direct product | #564×#64408 |
| Fitting | #564×C73 ⋊ C4 |
| Sylow | C73 ⋊ C4×#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×#64408 |
| commutator, socle | C22×C73 | C24×C4 |
| Fitting | #564×C73 | C4 |
| prime radical, cosocle | C22×D73 | C25 |
| hypercenter | #564 | #64408 |
| hypocenter | C73 | C4×#564 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ #564 | |
1800 conjugacy classes of subgroups; only the 776 normal subgroups are shown.
This group has 1800 conjugacy classes of subgroups — too many to draw. Only its 776 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4672 |
418 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1114466);