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C7×#19129749 #50303885

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

Aliases

direct productC7×#19129749

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C3×C4
derivedC5×C7×C13 ⋊ C3×C4×C7
HallC7×C7⋊#63121 ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C4
HallC72×C13⋊C3 ⋊ AGL(1,𝔽5)
HallC72×C13 ⋊ C3×AGL(1,𝔽5)
HallC5×C72 ⋊ AGL(1,𝔽13)
HallC5×C13⋊C3 ⋊ C7×Dic7
HallC5×C13 ⋊ C3×C7×Dic7
SylowC72 ⋊ #63121⋊C3
HallC13⋊C3 ⋊ C7×C7⋊AGL(1,𝔽5)
SylowC13 ⋊ C3×C7×C7⋊AGL(1,𝔽5)
SylowC5 ⋊ C7×#11763979

Subgroups

subgroupG/H
center, hypercenterC7#19129749
commutator, hypocenterC5×C7×C13C3×C4×C7
FrattiniC1G
Fitting, socleC5×C72×C13C3×C4
prime radicalC72×C5⋊(D13⋊C3)C2
cosocleC7×D65C2×C3×C7
LCSG ▷ C5×C7×C13
UCSC1 ◁ C7

144 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 36 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) = 910

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 571);