Finite Group Databasebeta

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H(3,𝔽4)×Dic71 #32160158

order18176
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C26×C42

Aliases

direct productH(3,𝔽4)×Dic71

Splittings

SylowC71 ⋊ C4×H(3,𝔽4)

Subgroups

subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
Fitting, prime radicalC2×H(3,𝔽4)×C71C2
socle, cosocleC23×C71C25
hypercenterC2×H(3,𝔽4)D71
hypocenterC71C4×H(3,𝔽4)
LCSG ▷ C22×C71 ▷ C71
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) = 4544

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 332274);