Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #107×C97 ⋊ C2 |
| Sylow | C97 ⋊ #428 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D97 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #107×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | #107 | D97 |
| hypocenter | C97 | #428 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #107 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=e,b^2=d,d^2=f,b^a=bd,d^a=df,c^b=cf,g^b=g^96,g^c=g^96694 conjugacy classes — view the full character table.
| maximal subgroup of | #428×D97, C2×#20260776, #27150323, … |
| maximal normal subgroup of | #428×D97, C2×#20260776, #27150323, … |
| maximal quotient of | #27140487, #27140502, #27140520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 590);