Finite Group Databasebeta

C2×#21432622 #29452239

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#21432622

Splittings

SylowC59 ⋊ C2×#2897

Subgroups

subgroupG/H
centerC23C22×C22⋊D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
Fitting, prime radicalC22×H(5,𝔽2)×C59C2
socleC23×C59C22×D4
cosocleC2×C4×C59C25
hypercenterC22×H(5,𝔽2)D59
hypocenterC59C2×#2897
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×H(5,𝔽2)

5226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1033118);