Finite Group Databasebeta

C2×#21424504 #28590302

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21424504

Splittings

FittingC2×C59×#518 ⋊ C2
SylowC59 ⋊ C2×#1889

Subgroups

subgroupG/H
centerC23#14273696
commutatorC23×C59C23×C4
FrattiniC24C23×D59
FittingC2×C59×#518C2
socleC23×C59#120
prime radicalC22×#14273695C2
cosocleC24×C59C24
hypercenterC2×#518D59
hypocenterC59C2×#1889
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C25 ◁ C2×#518

3566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

2036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 171181);