Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C97 ⋊ C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#87604 |
| commutator | C2×C97 | C22×C8 |
| Fitting | C22⋊C4×C97 | C4 |
| socle | C22×C97 | C22×C4 |
| hypercenter | C22⋊C4 | #87604 |
| hypocenter | C97 | C8×D4 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,97|a^2=e,c^2=e,e^2=f,b^a=bd,g^a=g^75,g^c=g^22,g^e=g^96280 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20261762, D4×#13095519, #27158450, … |
| maximal normal subgroup of | C2×#20261762, D4×#13095519, #27158450, … |
| maximal quotient of | #27157316, #27157319, #27157320, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1576);