Finite Group Databasebeta

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C4×C17×C163⋊C3 #45685261

order33252
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×C163⋊C3
unambiguous semidirect product(C4×C163)⋊(C3×C17)
unambiguous semidirect product(C4×C17×C163)⋊C3

Splittings

Fitting, HallC4×C17×C163 ⋊ C3
derived, SylowC163 ⋊ C3×C4×C17
HallC17×C163 ⋊ C3×C4
HallC4×C163 ⋊ C3×C17

Subgroups

subgroupG/H
center, hypercenterC4×C17C163⋊C3
commutator, hypocenterC163C3×C4×C17
FrattiniC2C2×C17×C163⋊C3
FittingC4×C17×C163C3
socleC2×C17×C163C2×C3
prime radicalC2×C17×C163⋊C3C2
cosocleC2×C163C2×C3×C17
LCSG ▷ C163
UCSC1 ◁ C4×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11084

Conjugacy classes & character table

3876 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33252, 2);