Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #104×C97 ⋊ C2 |
| Sylow | C97 ⋊ #421 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D4×D97 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #104×C97 | C2 |
| socle | C2×C97 | C2×C22⋊C4 |
| hypercenter | #104 | D97 |
| hypocenter | C97 | #421 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #104 | |
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,97|a^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,c^b=cf,d^b=df,g^c=g^96694 conjugacy classes — view the full character table.
| maximal subgroup of | #421×D97, C2×#20260750, #27150280, … |
| maximal normal subgroup of | #421×D97, C2×#20260750, #27150280, … |
| maximal quotient of | #27140120, #27140122, #27140125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 564);