Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C103 ⋊ C2 |
| Sylow | C103 ⋊ #436 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D103 |
| commutator, socle | C22×C103 | C22×C4 |
| Fitting | C4⋊C8×C103 | C2 |
| hypercenter | C4⋊C8 | D103 |
| hypocenter | C103 | #436 |
| LCS | G ▷ C22×C103 ▷ C103 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
122 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,103|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,c^b=cf,g^b=g^102,g^c=g^1021048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27193970, #27193972, #27193984, … |
| maximal normal subgroup of | #27193970, #27193972, #27193984, … |
| maximal quotient of | #27194028, #27194033, #27194040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 626);