Finite Group DatabasebetaFinite Group Databasebeta| order | 21376 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×C167⋊C32 |
| derived, Sylow | C167 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D167 |
| commutator, hypocenter | C167 | C22×C32 |
| Frattini | C16 | C22×D167 |
| Fitting | C22×C16×C167 | C2 |
| socle, prime radical | C23×C167 | C16 |
| cosocle | C16×C167 | C23 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21376 |
5440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 6799);