Finite Group Databasebeta

C2×#21454298 #30543508

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#21454298

Splittings

SylowC61 ⋊ C2×#2888

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic61
commutatorC22×C61C24×C4
FrattiniC2×C4C24×D61
Fitting, prime radicalC22×H(5,𝔽2)×C61C2
socleC22×C61C22×C22⋊C4
cosocleC2×C4×C61C25
hypercenterC22×H(5,𝔽2)D61
hypocenterC61C2×#2888
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×#41 ◁ C22×H(5,𝔽2)

5114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

2122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1033063);