Finite Group Databasebeta

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H(3,𝔽4)×#64408 #34030880

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C26×C42

Aliases

direct productH(3,𝔽4)×#64408

Splittings

FittingH(3,𝔽4)×C73 ⋊ C4
SylowC73 ⋊ C4×H(3,𝔽4)

Subgroups

subgroupG/H
center, FrattiniC22C24×#64408
commutator, socleC22×C73C24×C4
FittingH(3,𝔽4)×C73C4
prime radicalH(3,𝔽4)×D73C2
cosocleC22×D73C25
hypercenterH(3,𝔽4)#64408
hypocenterC73C4×H(3,𝔽4)
LCSG ▷ C22×C73 ▷ C73
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) = 1168

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1114464);