Finite Group DatabasebetaFinite Group Databasebeta| order | 848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#6157 |
| commutator, socle | C2×C53 | C2×C4 |
| Fitting, prime radical | C22×C53 | C4 |
| cosocle | Dic53 | C22 |
| hypercenter | C22 | #6157 |
| hypocenter | C53 | M16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C22 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
Polycyclic presentation:
2^4,53|a^2=c,c^2=d,b^a=bd,e^a=e^30,e^c=e^5262 conjugacy classes — view the full character table.
| maximal subgroup of | #13133277, #13133278, C2×#11719940, … |
| maximal normal subgroup of | #13133277, #13133278, C2×#11719940, … |
| maximal quotient of | #13133272, C22⋊#88324, #13133284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(848, 33);