Finite Group Databasebeta

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C32×C5×C13×#261 #44478211

order30420
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C13 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C13×#261

Splittings

Fitting, socle, HallC32×C5×C132 ⋊ C4
derivedC13 ⋊ C32×C4×C5×C13
HallC32×C132 ⋊ C4×C5
HallC5×C132 ⋊ C32×C4
SylowC132 ⋊ C32×C4×C5

Subgroups

subgroupG/H
center, hypercenterC32×C5×C13#261
commutator, hypocenterC13C32×C4×C5×C13
FrattiniC1G
Fitting, socleC32×C5×C132C4
prime radicalC32×C5×C13×D13C2
cosocleD13C2×C32×C5×C13
LCSG ▷ C13
UCSC1 ◁ C32×C5×C13

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2340

Conjugacy classes & character table

4095 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 800);