Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C97 ⋊ #442 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D97 |
| commutator | C4×C97 | C22×C4 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | C2×D8×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | C2×D8 | D97 |
| hypocenter | C97 | #442 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D8 | |
132 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=e,c^2=ef,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^96,d^b=df,g^c=g^96694 conjugacy classes — view the full character table.
| maximal subgroup of | #27143635, #27143637, #442×D97, … |
| maximal normal subgroup of | #27143635, #27143637, #442×D97, … |
| maximal quotient of | #27140560, #27140601, #27140650, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 661);