Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C97 ⋊ C4 |
| Sylow | C97 ⋊ #444 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#87604 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C4 | C22×#87604 |
| Fitting | Q16×C97 | C4 |
| socle | C2×C97 | C4×D4 |
| hypercenter | Q16 | #87604 |
| hypocenter | C97 | #444 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^22,d^b=df,g^b=g^96,g^c=g^22,g^e=g^96190 conjugacy classes — view the full character table.
| maximal subgroup of | #27158143, #27158144, #27158147, … |
| maximal normal subgroup of | #27158143, #27158144, #27158147, … |
| maximal quotient of | #27157326, #27157329, #27157334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1595);