Finite Group Databasebeta

C2×#21424050 #28587973

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

Aliases

direct productC2×#21424050

Splittings

SylowC59 ⋊ C2×#1792

Subgroups

subgroupG/H
centerC23#14273696
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC22×H(5,𝔽2)×C59C2
socleC23×C59#120
cosocleC22×C4×C59C24
hypercenterC22×H(5,𝔽2)D59
hypocenterC59C2×#1792
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×H(5,𝔽2)

4114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

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, 168852);