Finite Group Databasebeta

C2×#21437249 #29495215

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21437249

Splittings

FittingC2×C59×#504 ⋊ C2
SylowC59 ⋊ C2×#3417

Subgroups

subgroupG/H
centerC22C22×D472
commutator, cosocleC8×C59C25
FrattiniC8C24×D59
FittingC2×C59×#504C2
socleC22×C59C22×D8
hypercenterC2×#504D59
hypocenterC59C2×#3417
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ C2×#504

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

2384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076094);