Finite Group Databasebeta

C2×#21462814 #30626747

order15616
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×#21462814

Splittings

SylowC61 ⋊ C2×#3573

Subgroups

subgroupG/H
centerC22C24×#6923
commutatorC2×C61C25×C4
FrattiniC2C25×#6923
FittingC2×H(5,𝔽2)×C61C4
socleC22×C61C24×C4
prime radicalC2×#16840597C2
cosocleDic61C26
hypercenterC2×H(5,𝔽2)#6923
hypocenterC61C2×#3573
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×H(5,𝔽2)

10858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1116302);