Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C97 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #87604 |
| commutator, hypocenter | C97 | C2×C32 |
| Frattini | C8 | C2×#87604 |
| Fitting | C16×C97 | C4 |
| socle | C2×C97 | C2×C16 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C16 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^22,g^b=g^96,g^c=g^96448 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#87604, #27156842, #27156885, … |
| maximal normal subgroup of | C32×#87604, #27156842, #27156885, … |
| maximal quotient of | #27156841, #27156850, #27156894, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1480);