Finite Group Databasebeta

C2×#21461732 #30615125

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

Aliases

direct productC2×#21461732

Splittings

SylowC61 ⋊ C2×#1829

Subgroups

subgroupG/H
centerC22#16840705
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC23×C22⋊D61C22
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61C2×#1829
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4

1434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1104680);