Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of D72 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D72 |
| unambiguous semidirect product | (C7×D7)⋊C24 |
| unambiguous semidirect product | (C7⋊D7)⋊C24 |
| Fitting, socle | C23×C72 ⋊ C22 |
| derived, Sylow | C72 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D72 |
| commutator, cosocle, hypocenter | C72 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C23×C72 | C22 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C23 | |
1697 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#64423⋊C2, #72214948, C23×D7×AGL(1,𝔽7), … |
| maximal normal subgroup of | C23×#64423⋊C2, #72214948, C23×D7×AGL(1,𝔽7), … |
| maximal quotient of | #72214319, C22×#11716115, C22×D3×D72, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 925);