Finite Group Databasebeta

C22×#16837580 #29455297

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16837580

Splittings

SylowC59 ⋊ C22×#455

Subgroups

subgroupG/H
centerC23#14273696
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
Fitting, prime radicalC22×H(5,𝔽2)×C59C2
socleC23×C59#120
hypercenterC22×H(5,𝔽2)D59
hypocenterC59C22×#455
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×H(5,𝔽2)

5110 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, 1036176);