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D5×C11×#3861 #30633559

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productD5×C11×#3861
unambiguous semidirect productC5⋊(C2×C11×#3861)

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C2×C3
derived, HallC5×C72 ⋊ C2×C3×C11
HallC5×C11×#3861 ⋊ C2
HallC72×D5×C11 ⋊ C3
HallC5×#3861 ⋊ C2×C11
HallC72×C11 ⋊ C3×D5
HallC72×D5 ⋊ C3×C11
HallC5×C11 ⋊ C2×#3861
SylowC72 ⋊ C3×D5×C11
SylowC5 ⋊ C2×C11×#3861

Subgroups

subgroupG/H
center, hypercenterC11D5×#3861
commutator, cosocle, hypocenterC5×C72C2×C3×C11
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C5×C72
UCSC1 ◁ C11

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×AGL(1,𝔽5)×#3861, #3861×C11⋊AGL(1,𝔽5), C11×#15668765, …
maximal normal subgroup ofC11×AGL(1,𝔽5)×#3861, #3861×C11⋊AGL(1,𝔽5), C11×#15668765, …
maximal quotient ofC11×Dic5×#3861, C2×D5×C11×#3861

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 104);