Finite Group DatabasebetaFinite Group Databasebeta| order | 848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D53 |
| commutator | C2×C53 | C2×C4 |
| Fitting | C2×C4×C53 | C2 |
| socle, prime radical, cosocle | C22×C53 | C22 |
| hypercenter | C2×C4 | D53 |
| hypocenter | C53 | C4⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^4,53|a^2=d,b^2=c,b^a=bd,e^a=e^52218 conjugacy classes — view the full character table.
| maximal subgroup of | C4⋊C4×D53, C2×#11719919, #13133173, … |
| maximal normal subgroup of | C4⋊C4×D53, C2×#11719919, #13133173, … |
| maximal quotient of | #13133124, #13133146, #13133148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(848, 12);