Finite Group DatabasebetaFinite Group Databasebeta| order | 9872 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C617 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14578674 |
| commutator, socle | C2×C617 | C2×C4 |
| Fitting, prime radical | C22×C617 | C4 |
| cosocle | Dic617 | C22 |
| hypercenter | C22 | #14578674 |
| hypocenter | C617 | M16 |
| LCS | G ▷ C2×C617 ▷ C617 | |
| UCS | C1 ◁ C2 ◁ C22 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,617|a^2=c,c^2=d,b^a=bd,e^a=e^194,e^c=e^616626 conjugacy classes — view the full character table.
| maximal subgroup of | #34089762, #34089763, C2×#23754609, … |
| maximal normal subgroup of | #34089762, #34089763, C2×#23754609, … |
| maximal quotient of | #34089757, C22⋊#19096928, #34089769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9872, 49);