Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #41×C97 ⋊ C4 |
| Sylow | C97 ⋊ #421 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×C22⋊#87604 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C4 | C22×#87604 |
| Fitting | #41×C97 | C4 |
| socle | C2×C97 | C2×C22⋊C4 |
| hypercenter | #41 | #87604 |
| hypocenter | C97 | #421 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #41 | |
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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,g^a=g^22,c^b=cf,d^b=df,g^e=g^96262 conjugacy classes — view the full character table.
| maximal subgroup of | #27157584, #27157585, #27157622, … |
| maximal normal subgroup of | #27157584, #27157585, #27157622, … |
| maximal quotient of | #27157031, #27157033, #27157036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1546);