Finite Group Databasebeta

C42×D4×D61 #29838201

order15616
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC42×D4×D61

Splittings

FittingC42×D4×C61 ⋊ C2
SylowC61 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC2×C42C22×D61
commutatorC2×C61C23×C42
FrattiniC23C24×D61
FittingC42×D4×C61C2
socle, cosocleC23×C61C25
prime radicalC22×D4×D61C22
hypercenterC42×D4D61
hypocenterC61C2×C42×D4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C42 ◁ C42×D4

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 327756);