Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C97 ⋊ C2 |
| Sylow | C97 ⋊ B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15690779 |
| commutator | C23×C97 | C23 |
| Frattini | C23 | C22×D97 |
| Fitting | H(5,𝔽2)×C97 | C2 |
| socle | C2×C97 | #120 |
| hypercenter | H(5,𝔽2) | D97 |
| hypocenter | C97 | B(4,𝔽2) |
| LCS | G ▷ C23×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ H(5,𝔽2) | |
198 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|b^a=bd,c^a=ce,g^a=g^96,e^b=ef,d^c=df832 conjugacy classes — view the full character table.
| maximal subgroup of | #27143718, #27143719, #27143723, … |
| maximal normal subgroup of | #27143718, #27143719, #27143723, … |
| maximal quotient of | #27140654, #27140659, #27140665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 736);