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C3×C7⋊(C7⋊#63120) #50304362

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

Aliases

direct productC3×C7⋊(C7⋊#63120)

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derived, HallC5×C72×C13 ⋊ C3×C4
HallC3×C72×C13 ⋊ AGL(1,𝔽5)
HallC3×C5×C72 ⋊ Dic13
HallC72×C13 ⋊ C3×AGL(1,𝔽5)
HallC5×C72 ⋊ C3×Dic13
HallC3×C5×C13 ⋊ C7⋊Dic7
HallC3×C72 ⋊ #63120
HallC5×C13 ⋊ C3×C7⋊Dic7
SylowC72 ⋊ C3×#63120
HallC3×C13 ⋊ C7⋊(C7⋊AGL(1,𝔽5))
HallC3×C5 ⋊ C7⋊Dic91
SylowC13 ⋊ C3×C7⋊(C7⋊AGL(1,𝔽5))
SylowC5 ⋊ C3×C7⋊Dic91

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(C7⋊#63120)
commutator, hypocenterC5×C72×C13C3×C4
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C72×D5×C13C2
cosocleC72×D5×C13C2×C3
LCSG ▷ C5×C72×C13
UCSC1 ◁ C3

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

3831 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1048);