Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic412 |
| Sylow | C103 ⋊ C22×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D412 |
| commutator | C4×C103 | C24 |
| Frattini | C4 | C23×D103 |
| Fitting | C22×C8×C103 | C2 |
| socle | C23×C103 | D4 |
| hypercenter | C22×C8 | D103 |
| hypocenter | C103 | C22×Q16 |
| LCS | G ▷ C4×C103 ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
258 conjugacy classes of subgroups.
1660 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27195484, #27195486, #27196003, … |
| maximal normal subgroup of | #27195484, #27195486, #27196003, … |
| maximal quotient of | C22×#15692946, C22×#15692955, C2×C4×Dic412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 1326);