Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C103 ⋊ C2 |
| Sylow | C103 ⋊ #497 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D412 |
| commutator | C2×C4×C103 | C23 |
| Frattini | C2×C4 | C22×D103 |
| Fitting | #97×C103 | C2 |
| socle | C22×C103 | C2×D4 |
| hypercenter | #97 | D103 |
| hypocenter | C103 | #497 |
| LCS | G ▷ C2×C4×C103 ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
124 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,103|a^2=f,b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^102,c^b=cf1036 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27194452, #27194457, #27194463, … |
| maximal normal subgroup of | #27194452, #27194457, #27194463, … |
| maximal quotient of | #27194766, #27194777, #27194790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 943);