Finite Group Databasebeta

C2×#21445858 #29679629

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

Aliases

direct productC2×#21445858

Splittings

FittingC22×#108×C61 ⋊ C2
SylowC61 ⋊ C2×#1811

Subgroups

subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC22×#108×C61C2
socleC23×C61C2×C4⋊C4
prime radicalC24×D61Q8
cosocleC22×C4×C61C24
hypercenterC22×#108D61
hypocenterC61C2×#1811
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#108

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

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, 169184);