Finite Group DatabasebetaFinite Group Databasebeta| order | 22592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C353 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #19150751 |
| commutator, hypocenter | C353 | C2×C32 |
| Frattini | C2 | C2×#19150751 |
| Fitting | C4×C353 | C16 |
| socle | C2×C353 | C2×C16 |
| prime radical | C2×D353 | C16 |
| cosocle | #19150749 | C22 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C4 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11296 |
Polycyclic presentation:
2^6,353|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^304,g^b=g^352,g^c=g^283,g^d=g^311,g^e=g^352152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22592, 1678);