Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C97 ⋊ #436 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D97 |
| commutator, socle | C22×C97 | C22×C4 |
| Fitting | C4×D4×C97 | C2 |
| hypercenter | C4×D4 | D97 |
| hypocenter | C97 | #436 |
| LCS | G ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
122 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^96,c^b=cf,g^c=g^96988 conjugacy classes — view the full character table.
| maximal subgroup of | #27140566, #27140568, #27140580, … |
| maximal normal subgroup of | #27140566, #27140568, #27140580, … |
| maximal quotient of | #27140621, #27140627, #27140633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 627);