Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C97 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×#11715906 |
| commutator, socle | C2×C97 | C22×C8 |
| Frattini | C2 | C22×#11715906 |
| Fitting | C2×C4×C97 | C8 |
| hypercenter | C2×C4 | #11715906 |
| hypocenter | C97 | C2×M32 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^64,g^c=g^96,g^d=g^22,g^e=g^96136 conjugacy classes — view the full character table.
| maximal subgroup of | #27158808, #27158809, #27158810, … |
| maximal normal subgroup of | #27158808, #27158809, #27158810, … |
| maximal quotient of | #27158892, C4×#15690906, C4×#15690907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1668);