Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D97⋊#131 |
| Sylow | C97 ⋊ C2×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#87604 |
| commutator, socle | C2×C97 | C23×C4 |
| Frattini | C2 | C23×#87604 |
| Fitting | #41×C97 | C4 |
| hypercenter | #41 | #87604 |
| hypocenter | C97 | C2×#131 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ #41 | |
266 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=e,e^2=f,g^a=g^22,c^b=cf,g^d=g^96,g^e=g^96280 conjugacy classes — view the full character table.
| maximal subgroup of | #27157512, #27157516, #27157775, … |
| maximal normal subgroup of | #27157512, #27157516, #27157775, … |
| maximal quotient of | #27158296, C4×#15690897, C4×#15690898, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1625);