Finite Group Databasebeta

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C3×C5×C72×#261 #50304339

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC3×C5×C72×#261

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C4
derived, SylowC13 ⋊ C3×C4×C5×C72
HallC5×C72×C13 ⋊ C3×C4
HallC3×C72×C13 ⋊ C4×C5
HallC72×C13 ⋊ C3×C4×C5
HallC3×C5×C13 ⋊ C4×C72
HallC5×C13 ⋊ C3×C4×C72
HallC3×C13 ⋊ C4×C5×C72

Subgroups

subgroupG/H
center, hypercenterC3×C5×C72#261
commutator, hypocenterC13C3×C4×C5×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C13C4
prime radicalC3×C5×C72×D13C2
cosocleD13C2×C3×C5×C72
LCSG ▷ C13
UCSC1 ◁ C3×C5×C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

5145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1025);