Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#15693010 |
| Fitting | C22×Q8×C103 ⋊ C2 |
| Sylow | C103 ⋊ C2×#124 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D103 |
| commutator | C22×C103 | C24 |
| Frattini | C22 | C23×D103 |
| Fitting | C22×Q8×C103 | C2 |
| socle | C23×C103 | C23 |
| hypercenter | C22×Q8 | D103 |
| hypocenter | C103 | C2×#124 |
| LCS | G ▷ C22×C103 ▷ C103 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
330 conjugacy classes of subgroups.
1048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27195529, #27195545, #27195547, … |
| maximal normal subgroup of | #27195529, #27195545, #27195547, … |
| maximal quotient of | C2×#20267656, C2×#20267681, C2×#20267692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 1067);