Finite Group Databasebeta

C2×#21432796 #29452550

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

Aliases

direct productC2×#21432796

Splittings

FittingC2×C59×#436 ⋊ C2
SylowC59 ⋊ C2×#2930

Subgroups

subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#436C2
socleC23×C59C23×C4
prime radicalC2×#16837911C2
cosocleC2×C4×C59C25
hypercenterC2×#436D59
hypocenterC59C2×#2930
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#436

2870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1712 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033429);