Finite Group Databasebeta

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H(3,𝔽4)×Dic79 #34450975

order20224
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C26×C42

Aliases

direct productH(3,𝔽4)×Dic79

Splittings

SylowC79 ⋊ C4×H(3,𝔽4)

Subgroups

subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
Fitting, prime radicalC2×H(3,𝔽4)×C79C2
socle, cosocleC23×C79C25
hypercenterC2×H(3,𝔽4)D79
hypocenterC79C4×H(3,𝔽4)
LCSG ▷ C22×C79 ▷ C79
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) = 5056

Conjugacy classes & character table

1558 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 332274);