Finite Group Databasebeta

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C5×#21439560 #50303603

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

Aliases

direct productC5×#21439560

Splittings

derived, HallC72×C13 ⋊ C3×C4×C5
HallC5×C7⋊Dic91 ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C4
HallC5×C72×C13 ⋊ C3×C4
HallC7⋊Dic91 ⋊ C3×C5
HallC72×C13⋊C3 ⋊ C4×C5
HallC5×C72 ⋊ Dic13⋊C3
HallC5×C13⋊C3 ⋊ C7⋊Dic7
HallC5×C13 ⋊ C3×C7⋊Dic7
SylowC72 ⋊ C5×Dic13⋊C3
HallC13⋊C3 ⋊ C5×C7⋊Dic7
SylowC13 ⋊ C3×C5×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C5(C13⋊C3)⋊(C7⋊D7)
commutator, hypocenterC72×C13C3×C4×C5
FrattiniC2C5×(C13⋊C3)⋊(C7⋊D7)
Fitting, socleC2×C5×C72×C13C2×C3
prime radicalC2×C5×C72×C13⋊C3C2
cosocleC2×C72×C13C2×C3×C5
LCSG ▷ C72×C13
UCSC1 ◁ C2×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12740

Conjugacy classes & character table

1760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 289);