Finite Group DatabasebetaFinite Group Databasebeta| order | 848 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C53 ⋊ C2 |
| Sylow | C53 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D53 |
| commutator, socle, cosocle | C2×C53 | C23 |
| Frattini | C2 | C22×D53 |
| Fitting | C2×C4×C53 | C2 |
| hypercenter | C2×C4 | D53 |
| hypocenter | C53 | #41 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
Polycyclic presentation:
2^4,53|b^2=d,c^a=cd,e^a=e^52218 conjugacy classes — view the full character table.
| maximal subgroup of | #13133143, #13133145, #13133223, … |
| maximal normal subgroup of | #13133143, #13133145, #13133223, … |
| maximal quotient of | #13133174, #13133176, C4×C22⋊D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(848, 38);