Finite Group Databasebeta

← Prev (#30608709) Next (#30608711) →

C4⋊C4×C22⋊#6923 #30608710

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC4⋊C4×C22⋊#6923

Splittings

FittingC22×C4⋊C4×C61 ⋊ C4
SylowC61 ⋊ C22⋊C4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×#6923
commutatorC22×C61C22×C42
FittingC22×C4⋊C4×C61C4
socleC23×C61C23×C4
prime radicalC24×D61C23
cosocleC23×D61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61C22⋊C4×C4⋊C4
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4⋊C4

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1098265);