Finite Group Databasebeta

C2×#21460909 #30606283

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

Aliases

direct productC2×#21460909

Splittings

SylowC61 ⋊ C2×#1392

Subgroups

subgroupG/H
centerC22#16840639
commutatorC23×C61C2×C42
FrattiniC2×D4C22×#6923
FittingC2×#100×C61C4
socleC22×C61#342
prime radicalC22×#11758224C22
cosocleC2×#11758224C23
hypercenterC2×#100#6923
hypocenterC61C2×#1392
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#100

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1095838);