Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C103 ⋊ #347 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×Dic103 |
| commutator | C4×C103 | C42 |
| Frattini | C2×C8 | C2×D103 |
| Fitting | #97×C103 | C2 |
| socle | C2×C103 | #97 |
| hypercenter | #97 | D103 |
| hypocenter | C103 | #347 |
| LCS | G ▷ C4×C103 ▷ C103 | |
| UCS | C1 ◁ C4 ◁ #97 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,103|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,g^a=g^102,c^b=cf1042 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27193176, #27193177, #27193178, … |
| maximal normal subgroup of | #27193176, #27193177, #27193178, … |
| maximal quotient of | #27193065, #27193224, C2×#20267569 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 327);