Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C26 |
| direct product | C5×D4×C22⋊D5 |
| Fitting | C22×C52×D4 ⋊ C2 |
| Sylow | C52 ⋊ D42 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C23×D5 |
| commutator, cosocle | C22×C5 | C24×C5 |
| Frattini | C22 | C23×C5×D5 |
| Fitting | C22×C52×D4 | C2 |
| socle | C22×C52 | C24 |
| hypercenter | C22×C5×D4 | D5 |
| hypocenter | C5 | C5×D42 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C5 ◁ C22×C5×D4 | |
1092 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
325 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×#87886, C5×#10618096, #72258480 |
| maximal normal subgroup of | D4×#87886, C5×#10618096, #72258480 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9309);