Finite Group Databasebeta

#135×D52 #16738219

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct product#135×D52

Splittings

FittingC4×C13×#135 ⋊ C2
SylowC13 ⋊ D4×#135

Subgroups

subgroupG/H
centerC2×C4C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC4×C13×#135C2
socleC22×C13C23×D4
hypercenterC4×#135D13
hypocenterC13D4×#135
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#135

2822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

406 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1044868);