Finite Group Databasebeta

C2×#21424695 #28590933

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

Aliases

direct productC2×#21424695

Splittings

SylowC59 ⋊ C2×#1922

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#405C2
socleC23×C59C4×D4
prime radicalC24×C59#41
cosocleC22×C4×C59C24
hypercenterC2×#405D59
hypocenterC59C2×#1922
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C23×C8 ◁ C2×#405

854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 171812);