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C3×ΓL(1,𝔽32)⋊Dic17 #44539265

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×ΓL(1,𝔽32)⋊Dic17
unambiguous semidirect product(C3×Dic527)⋊C5

Splittings

derived, HallC17×C31 ⋊ C3×C4×C5
HallC3×C17×ΓL(1,𝔽32) ⋊ C4
HallC3×Dic527 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C3×C4
HallDic527 ⋊ C3×C5
HallC3×C17×C31 ⋊ C4×C5
HallC3×ΓL(1,𝔽32) ⋊ Dic17
HallΓL(1,𝔽32) ⋊ C3×Dic17
HallC3×C31 ⋊ C5×Dic17
HallC3×C17 ⋊ Dic31⋊C5
SylowC31 ⋊ C3×C5×Dic17
SylowC17 ⋊ C3×Dic31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C17⋊(D31⋊C5)
commutator, hypocenterC17×C31C3×C4×C5
FrattiniC2C3×C17⋊(D31⋊C5)
Fitting, socleC2×C3×C17×C31C2×C5
prime radicalC2×C3×C17×ΓL(1,𝔽32)C2
cosocleC2×C17×C31C2×C3×C5
LCSG ▷ C17×C31
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6324

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 22);