Finite Group Databasebeta

C2×#21446057 #29680908

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21446057

Splittings

SylowC61 ⋊ C2×#1861

Subgroups

subgroupG/H
centerC2×C4#14519745
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#421C2
socleC22×C61#385
prime radicalC22×#41×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#421D61
hypocenterC61C2×#1861
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

1358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

1384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 170463);