Finite Group Databasebeta

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C4×C5×C7×#63271 #50303674

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C7×#63271

Splittings

Fitting, HallC4×C5×C72×C13 ⋊ C3
derivedC7×C13 ⋊ C3×C4×C5×C7
HallC5×C72×C13 ⋊ C3×C4
HallC4×C72×C13 ⋊ C3×C5
HallC4×C5×C72 ⋊ C13⋊C3
HallC72×C13 ⋊ C3×C4×C5
HallC4×C5×C13 ⋊ C7×ΓL(1,𝔽8)
HallC5×C72 ⋊ C4×C13⋊C3
HallC4×C72 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C4×C7×ΓL(1,𝔽8)
HallC4×C13 ⋊ C5×C7×ΓL(1,𝔽8)
SylowC72 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C4×C5×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC4×C5×C7#63271
commutator, hypocenterC7×C13C3×C4×C5×C7
FrattiniC2C2×C5×C7×#63271
FittingC4×C5×C72×C13C3
socleC2×C5×C72×C13C2×C3
prime radicalC2×C5×C7×#63271C2
cosocleC2×C7×C13C2×C3×C5×C7
LCSG ▷ C7×C13
UCSC1 ◁ C4×C5×C7

120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 5460

Conjugacy classes & character table

4620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 360);