Finite Group Databasebeta

C2×#21424375 #28589768

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21424375

Splittings

FittingC2×C59×#385 ⋊ C2
SylowC59 ⋊ C2×#1867

Subgroups

subgroupG/H
centerC23#14273695
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC2×C59×#385C2
socleC23×C59#120
prime radicalC23×C22⋊D59C22
cosocleC24×C59C24
hypercenterC2×#385D59
hypocenterC59C2×#1867
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C25 ◁ C2×#385

1994 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 170647);