Finite Group Databasebeta

C2×#21460879 #30606197

order15616
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#21460879

Splittings

SylowC61 ⋊ C2×#1381

Subgroups

subgroupG/H
centerC23#14519846
commutatorC8×C61C2×C42
FrattiniC2×C8C22×#6923
FittingC22×C16×C61C4
socleC23×C61#107
prime radicalC23×D61Q16
cosocleC2×C8×D61C23
hypercenterC22×C16#6923
hypocenterC61C2×#1381
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1048 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1095752);