Finite Group Databasebeta

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C17×(C163⋊C3)⋊C4 #45685269

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

Aliases

direct productC17×(C163⋊C3)⋊C4
unambiguous semidirect product(C163⋊C3)⋊(C4×C17)
unambiguous semidirect productDic163⋊(C3×C17)
unambiguous semidirect product(C17×Dic163)⋊C3

Splittings

derived, SylowC163 ⋊ C3×C4×C17
HallC17×Dic163 ⋊ C3
HallC17×C163⋊C3 ⋊ C4
HallC17×C163 ⋊ C3×C4
HallDic163 ⋊ C3×C17
HallC163⋊C3 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D163⋊C3
commutator, hypocenterC163C3×C4×C17
FrattiniC2C17×D163⋊C3
Fitting, socleC2×C17×C163C2×C3
prime radicalC2×C17×C163⋊C3C2
cosocleC2×C163C2×C3×C17
LCSG ▷ C163
UCSC1 ◁ C2×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11084

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33252, 10);