Finite Group Databasebeta

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C11×(C163⋊C3)⋊C4 #36340211

order21516
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×(C163⋊C3)⋊C4
unambiguous semidirect product(C163⋊C3)⋊(C4×C11)
unambiguous semidirect productDic163⋊(C3×C11)
unambiguous semidirect product(C11×Dic163)⋊C3

Splittings

derived, SylowC163 ⋊ C3×C4×C11
HallC11×Dic163 ⋊ C3
HallC11×C163⋊C3 ⋊ C4
HallC11×C163 ⋊ C3×C4
HallDic163 ⋊ C3×C11
HallC163⋊C3 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11D163⋊C3
commutator, hypocenterC163C3×C4×C11
FrattiniC2C11×D163⋊C3
Fitting, socleC2×C11×C163C2×C3
prime radicalC2×C11×C163⋊C3C2
cosocleC2×C163C2×C3×C11
LCSG ▷ C163
UCSC1 ◁ C2×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7172

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21516, 10);