Finite Group Databasebeta

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C3×C5×C13×#5997 #50304336

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C13 · Schur multiplier (H2) = C7

Aliases

direct productC3×C5×C13×#5997

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derived, SylowC72 ⋊ C3×C4×C5×C13
HallC5×C72×C13 ⋊ C3×C4
HallC3×C72×C13 ⋊ C4×C5
HallC3×C5×C72 ⋊ C4×C13
HallC72×C13 ⋊ C3×C4×C5
HallC5×C72 ⋊ C3×C4×C13
HallC3×C72 ⋊ C4×C5×C13

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13#5997
commutator, hypocenterC72C3×C4×C5×C13
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C5×C13×C7⋊D7C2
cosocleC7⋊D7C2×C3×C5×C13
LCSG ▷ C72
UCSC1 ◁ C3×C5×C13

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

3120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1022);