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 | C4 | C2×D53 |
| commutator, socle | C2×C53 | C2×C4 |
| Fitting | C2×C4×C53 | C2 |
| prime radical | C22×C53 | C4 |
| cosocle | C4×C53 | C22 |
| hypercenter | C2×C4 | D53 |
| hypocenter | C53 | M16 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
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^52218 conjugacy classes — view the full character table.
| maximal subgroup of | #13133133, #13133134, #13133135, … |
| maximal normal subgroup of | #13133133, #13133134, #13133135, … |
| maximal quotient of | #13133128, C22⋊#88322, C4⋊#88322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(848, 10);