Finite Group Databasebeta

#534×Dic61 #29839030

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#534×Dic61

Splittings

SylowC61 ⋊ C4×#534

Subgroups

subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
Fitting, prime radicalC2×C61×#534C2
socle, cosocleC23×C61C25
hypercenterC2×#534D61
hypocenterC61C4×#534
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#534

3770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 328585);