Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#6157 |
| commutator, socle | C2×C53 | C22×C8 |
| Fitting | M16×C53 | C4 |
| prime radical | #11719945 | C4 |
| cosocle | #88322 | C23 |
| hypercenter | M16 | #6157 |
| hypocenter | C53 | #504 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ M16 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^6,53|a^2=d,d^2=e,e^2=f,g^a=g^30,c^b=cf,g^b=g^52,g^d=g^52170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 1608);