Finite Group Databasebeta

← Prev (#30624908) Next (#30624910) →

H(3,𝔽4)×#6923 #30624909

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C26×C42

Aliases

direct productH(3,𝔽4)×#6923

Splittings

FittingC61×H(3,𝔽4) ⋊ C4
SylowC61 ⋊ C4×H(3,𝔽4)

Subgroups

subgroupG/H
center, FrattiniC22C24×#6923
commutator, socleC22×C61C24×C4
FittingC61×H(3,𝔽4)C4
prime radicalH(3,𝔽4)×D61C2
cosocleC22×D61C25
hypercenterH(3,𝔽4)#6923
hypocenterC61C4×H(3,𝔽4)
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ H(3,𝔽4)

2664 conjugacy classes of subgroups; only the 776 normal subgroups are shown.

normal subgroups only

This group has 2664 conjugacy classes of subgroups — too many to draw. Only its 776 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114464);