Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C103 ⋊ #424 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D103 |
| commutator, socle | C22×C103 | C22×C4 |
| Fitting | C22×C8×C103 | C2 |
| hypercenter | C22×C8 | D103 |
| hypocenter | C103 | #424 |
| LCS | G ▷ C22×C103 ▷ C103 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C8 | |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,103|a^2=e,b^2=d,e^2=f,b^a=bd,c^b=cf,g^b=g^1021660 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27193085, #27195419, #27195422, … |
| maximal normal subgroup of | #27193085, #27195419, #27195422, … |
| maximal quotient of | #27193914, #27193918, #27193922, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 575);