Finite Group DatabasebetaFinite Group Databasebeta| order | 22592 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | 2−1+4×C353 ⋊ C2 |
| Sylow | C353 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D353 |
| commutator, socle, cosocle | C2×C353 | C25 |
| Fitting | 2−1+4×C353 | C2 |
| hypercenter | 2−1+4 | D353 |
| hypocenter | C353 | #585 |
| LCS | G ▷ C2×C353 ▷ C353 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
810 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5648 |
Polycyclic presentation:
2^6,353|e^2=f,b^a=bf,d^a=df,c^b=cf,g^c=g^352,g^d=g^352,g^e=g^3523026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22592, 1386);