Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C7 |
| direct product | C2×#11716129 |
| Fitting | C22×C4×C72 ⋊ C2 |
| Sylow | C72 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×C7⋊D7 |
| commutator, cosocle | C2×C72 | C24 |
| Frattini | C2 | C23×C7⋊D7 |
| Fitting | C22×C4×C72 | C2 |
| socle | C22×C72 | C23 |
| hypercenter | C22×C4 | C7⋊D7 |
| hypocenter | C72 | C2×#41 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
820 conjugacy classes of subgroups.
| transitive degree | μt(G) = 784 |
404 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#41×C7⋊D7, C2×#13096548, C2×#13096577, … |
| maximal normal subgroup of | C2×#41×C7⋊D7, C2×#13096548, C2×#13096577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 897);