Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C103 ⋊ #350 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22⋊D103 |
| commutator | C4×C103 | C2×C8 |
| Frattini | C2×C8 | C2×D103 |
| Fitting | #131×C103 | C2 |
| socle | C2×C103 | C22⋊C8 |
| hypercenter | #131 | D103 |
| hypocenter | C103 | #350 |
| LCS | G ▷ C4×C103 ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #131 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,103|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^102,c^b=cf,d^b=df1048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #350×D103, C2×#20267575, #27196770, … |
| maximal normal subgroup of | #350×D103, C2×#20267575, #27196770, … |
| maximal quotient of | #27193070, #27193086, D4⋊(C103⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 333);