Finite Group Databasebeta

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C32×C7×C19×AGL(1,𝔽5) #37561510

order23940
automorphism?
homologyAbelianization (H1) = C32×C4×C7×C19 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×C19×AGL(1,𝔽5)

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C4
derived, SylowC5 ⋊ C32×C4×C7×C19
HallC32×C5×C19 ⋊ C4×C7
HallC5×C7×C19 ⋊ C32×C4
HallC32×C5×C7 ⋊ C4×C19
HallC5×C19 ⋊ C32×C4×C7
HallC32×C5 ⋊ C4×C7×C19
HallC5×C7 ⋊ C32×C4×C19

Subgroups

subgroupG/H
center, hypercenterC32×C7×C19AGL(1,𝔽5)
commutator, hypocenterC5C32×C4×C7×C19
FrattiniC1G
Fitting, socleC32×C5×C7×C19C4
prime radicalC32×C7×D5×C19C2
cosocleD5C2×C32×C7×C19
LCSG ▷ C5
UCSC1 ◁ C32×C7×C19

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5985

Conjugacy classes & character table

5985 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 642);