Finite Group Databasebeta

C2×#21424245 #28588954

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21424245

Splittings

SylowC59 ⋊ C2×#1841

Subgroups

subgroupG/H
centerC2×C4#14273686
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C4×M16×C59C2
socleC22×C59#383
prime radicalC24×C59#41
cosocleC22×C4×C59C24
hypercenterC2×C4×M16D59
hypocenterC59C2×#1841
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ C2×C4×M16

730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 169833);