Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C103 ⋊ #364 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D412 |
| commutator | C4×C103 | C2×C8 |
| Frattini | C2×C8 | C2×D103 |
| Fitting | C4×C8×C103 | C2 |
| socle | C2×C103 | C4⋊C8 |
| hypercenter | C4×C8 | D103 |
| hypocenter | C103 | #364 |
| LCS | G ▷ C4×C103 ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ C4×C8 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,103|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^1021660 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27193117, #27193118, #27193120, … |
| maximal normal subgroup of | #27193117, #27193118, #27193120, … |
| maximal quotient of | #27193208, #27193214, #27193226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 370);