Finite Group Databasebeta

C2×#41×C59⋊C8 #29453123

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

Aliases

direct productC2×#41×C59⋊C8

Splittings

SylowC59 ⋊ C2×C8×#41

Subgroups

subgroupG/H
centerC2×C42C22×D59
commutatorC2×C59C24×C8
FrattiniC2×C4C24×D59
FittingC2×C4×#41×C59C2
socleC23×C59C23×C4
prime radicalC22×#41×C59C4
cosocleC2×C4×C59C25
hypercenterC2×C4×#41D59
hypocenterC59C2×C8×#41
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C42 ◁ C2×C4×#41

2566 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, 1034002);