Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q16×C97 ⋊ C4 |
| Sylow | C97 ⋊ #360 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15690872 |
| commutator | C8×C97 | C2×C4 |
| Frattini | C8 | C2×#87604 |
| Fitting | Q16×C97 | C4 |
| socle | C2×C97 | #102 |
| hypercenter | Q16 | #87604 |
| hypocenter | C97 | #360 |
| LCS | G ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^22,c^b=cef,d^b=df,e^b=ef,g^b=g^96,g^d=g^96184 conjugacy classes — view the full character table.
| maximal subgroup of | D97⋊#360, C2×#20261652, #27158056, … |
| maximal normal subgroup of | D97⋊#360, C2×#20261652, #27158056, … |
| maximal quotient of | #27156695, #27156696, #27156723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1466);