Finite Group Databasebeta

C2×#21425345 #28616447

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21425345

Splittings

FittingC2×C59×#386 ⋊ C2
SylowC59 ⋊ C2×#2044

Subgroups

subgroupG/H
centerC23#14273695
commutator, cosocleC24×C59C24
FrattiniC24C23×D59
FittingC2×C59×#386C2
socleC23×C59#120
prime radicalC2×#16837961C2
hypercenterC2×#386D59
hypocenterC59C2×#2044
LCSG ▷ C24×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C25 ◁ C2×#386

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 197326);