Finite Group Databasebeta

C8×#41×D59 #29453118

order15104
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC8×#41×D59

Splittings

FittingC8×#41×C59 ⋊ C2
SylowC59 ⋊ C2×C8×#41

Subgroups

subgroupG/H
centerC4×C8C22×D59
commutatorC2×C59C24×C8
FrattiniC2×C4C24×D59
FittingC8×#41×C59C2
socleC22×C59C24×C4
prime radicalC2×#41×D59C4
cosocleC2×C4×C59C25
hypercenterC8×#41D59
hypocenterC59C2×C8×#41
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C4×C8 ◁ C8×#41

2566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 1033997);