Finite Group Databasebeta

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H(3,𝔽4)×#6157 #28328988

order13568
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C26×C42

Aliases

direct productH(3,𝔽4)×#6157

Splittings

FittingC53×H(3,𝔽4) ⋊ C4
SylowC53 ⋊ C4×H(3,𝔽4)

Subgroups

subgroupG/H
center, FrattiniC22C24×#6157
commutator, socleC22×C53C24×C4
FittingC53×H(3,𝔽4)C4
prime radicalH(3,𝔽4)×D53C2
cosocleC22×D53C25
hypercenterH(3,𝔽4)#6157
hypocenterC53C4×H(3,𝔽4)
LCSG ▷ C22×C53 ▷ C53
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) = 848

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1114464);