Finite Group Databasebeta

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H(3,𝔽4)×Dic89 #36717134

order22784
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C26×C42

Aliases

direct productH(3,𝔽4)×Dic89

Splittings

SylowC89 ⋊ C4×H(3,𝔽4)

Subgroups

subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
Fitting, prime radicalC2×H(3,𝔽4)×C89C2
socle, cosocleC23×C89C25
hypercenterC2×H(3,𝔽4)D89
hypocenterC89C4×H(3,𝔽4)
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×H(3,𝔽4)

2664 conjugacy classes of subgroups; only the 1093 normal subgroups are shown.

normal subgroups only

This group has 2664 conjugacy classes of subgroups — too many to draw. Only its 1093 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) = 5696

Conjugacy classes & character table

1748 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 332274);