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C3×AGL(1,𝔽5)×C529 #44540672

order31740
automorphism?
homologyAbelianization (H1) = C3×C4×C529 · Schur multiplier (H2) = C1

Aliases

direct productC3×AGL(1,𝔽5)×C529

Splittings

Fitting, HallC3×C5×C529 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C529
HallC5×C529 ⋊ C3×C4
HallC3×C5 ⋊ C4×C529

Subgroups

subgroupG/H
center, hypercenterC3×C529AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C529
FrattiniC23C3×AGL(1,𝔽5)×C23
FittingC3×C5×C529C4
socleC3×C5×C23C4×C23
prime radicalC3×D5×C23C2×C23
cosocleD5×C23C2×C3×C23
LCSG ▷ C5
UCSC1 ◁ C3×C529

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7935

Conjugacy classes & character table

7935 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31740, 10);