Finite Group DatabasebetaFinite Group Databasebeta| order | 22112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C691 ⋊ C2 |
| Sylow | C691 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D691 |
| commutator, socle, cosocle | C2×C691 | C24 |
| Fitting | #41×C691 | C2 |
| hypercenter | #41 | D691 |
| hypocenter | C691 | H(5,𝔽2) |
| LCS | G ▷ C2×C691 ▷ C691 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5528 |
Polycyclic presentation:
2^5,691|b^a=be,d^a=de,c^b=ce,f^c=f^690,f^d=f^6903467 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22112, 192);