Finite Group Databasebeta

C2×#21460692 #30596798

order15616
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#21460692

Splittings

FittingC22×C4⋊C4×C61 ⋊ C4
SylowC61 ⋊ C2×#1294

Subgroups

subgroupG/H
centerC24C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC24×C61C22⋊C4
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1294
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1086353);