Finite Group DatabasebetaFinite Group Databasebeta| order | 22144 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C23×D4×D173 |
| Fitting | C23×D4×C173 ⋊ C2 |
| Sylow | C173 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D173 |
| commutator, cosocle | C2×C173 | C26 |
| Frattini | C2 | C25×D173 |
| Fitting | C23×D4×C173 | C2 |
| socle | C24×C173 | C23 |
| hypercenter | C23×D4 | D173 |
| hypocenter | C173 | C24×D4 |
| LCS | G ▷ C2×C173 ▷ C173 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
10552 conjugacy classes of subgroups; only the 3557 normal subgroups are shown.
This group has 10552 conjugacy classes of subgroups — too many to draw. Only its 3557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5536 |
3520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22144, 19301);