Finite Group Databasebeta

C2×#21425222 #28615921

order15104
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21425222

Splittings

FittingC2×C59×#379 ⋊ C2
SylowC59 ⋊ C2×#2021

Subgroups

subgroupG/H
centerC23#14273695
commutator, cosocleC24×C59C24
FrattiniC24C23×D59
FittingC2×C59×#379C2
socleC23×C59#120
hypercenterC2×#379D59
hypocenterC59C2×#2021
LCSG ▷ C24×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C25 ◁ C2×#379

3986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

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, 196800);