Finite Group Databasebeta

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H(5,𝔽2)×#3866 #18011577

order4736
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productH(5,𝔽2)×#3866

Splittings

FittingH(5,𝔽2)×C37 ⋊ C4
SylowC37 ⋊ C4×H(5,𝔽2)

Subgroups

subgroupG/H
center, FrattiniC2C24×#3866
commutator, socleC2×C37C24×C4
FittingH(5,𝔽2)×C37C4
prime radicalH(5,𝔽2)×D37C2
cosocleC2×D37C25
hypercenterH(5,𝔽2)#3866
hypocenterC37C4×H(5,𝔽2)
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ H(5,𝔽2)

1660 conjugacy classes of subgroups; only the 754 normal subgroups are shown.

normal subgroups only

This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 754 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) = 296

Conjugacy classes & character table

221 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 21491);