Finite Group Databasebeta

C2×#21432705 #29452385

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21432705

Splittings

SylowC59 ⋊ C2×#2916

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#568C2
socleC22×C59C22×C4⋊C4
prime radicalC22×#41×C59C22
cosocleC2×C4×C59C25
hypercenterC2×#568D59
hypocenterC59C2×#2916
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×#41 ◁ C2×#568

2586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033264);