Finite Group Databasebeta

#41×C59⋊C16 #28742208

order15104
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct product#41×C59⋊C16

Splittings

SylowC59 ⋊ C16×#41

Subgroups

subgroupG/H
centerC4×C8C22×D59
commutatorC2×C59C23×C16
FrattiniC2×C8C23×D59
FittingC8×#41×C59C2
socleC22×C59C23×C8
prime radicalC2×#41×C59C8
cosocleC2×C8×C59C24
hypercenterC8×#41D59
hypocenterC59C16×#41
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C4×C8 ◁ C8×#41

602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2480 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 323087);