Finite Group Databasebeta

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C3×C17×AGL(1,𝔽5)×C31 #44539338

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C17×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×AGL(1,𝔽5)×C31

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C17×C31
HallC5×C17×C31 ⋊ C3×C4
HallC3×C5×C31 ⋊ C4×C17
HallC3×C5×C17 ⋊ C4×C31
HallC5×C31 ⋊ C3×C4×C17
HallC5×C17 ⋊ C3×C4×C31
HallC3×C5 ⋊ C4×C17×C31

Subgroups

subgroupG/H
center, hypercenterC3×C17×C31AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C17×C31
FrattiniC1G
Fitting, socleC3×C5×C17×C31C4
prime radicalC3×D5×C17×C31C2
cosocleD5C2×C3×C17×C31
LCSG ▷ C5
UCSC1 ◁ C3×C17×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

7905 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 95);