Finite Group Databasebeta

C2×#21447345 #29709776

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21447345

Splittings

SylowC61 ⋊ C2×#2093

Subgroups

subgroupG/H
centerC24D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#102×C61C2
socleC24×C61C2×D4
prime radicalC23×D4×C61C22
hypercenterC22×#102D61
hypocenterC61C2×#2093
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 199331);