Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C4×C52 ⋊ C22 |
| Sylow | C52 ⋊ D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C22×C4×C52 | C22 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | D42 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
1092 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|d^2=e,c^a=cf,g^a=g^4,c^b=cf,d^b=de,h^b=h^4157 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#87886, #72258480, #72258510 |
| maximal normal subgroup of | D4×#87886, #72258480, #72258510 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 8517);