Finite Group Databasebeta

C2×#21446952 #29707280

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21446952

Splittings

FittingC22×C4⋊Q8×C61 ⋊ C2
SylowC61 ⋊ C2×#2023

Subgroups

subgroupG/H
centerC24C2×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×C4⋊Q8×C61C2
socleC24×C61C2×D4
prime radicalC23×D244C22
hypercenterC22×C4⋊Q8D61
hypocenterC61C2×#2023
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊Q8

1734 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, 196835);