Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C97 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#11715906 |
| commutator, socle | C2×C97 | C2×C16 |
| Fitting | C2×C4×C97 | C8 |
| hypercenter | C2×C4 | #11715906 |
| hypocenter | C97 | M64 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^64,g^c=g^22,g^d=g^96136 conjugacy classes — view the full character table.
| maximal subgroup of | #27158824, #27158825, #27158830, … |
| maximal normal subgroup of | #27158824, #27158825, #27158830, … |
| maximal quotient of | #27158821, C22⋊#15690900, C4⋊#15690900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1657);