Finite Group Databasebeta

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C2×C11⋊C5×#3861 #30633513

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11⋊C5×#3861
unambiguous semidirect product(C2×C11)⋊(C5×#3861)
unambiguous semidirect product(C2×C11×#3861)⋊C5

Splittings

Fitting, socle, HallC2×C72×C11 ⋊ C3×C5
derived, HallC72×C11 ⋊ C2×C3×C5
HallC2×C72×C11⋊C5 ⋊ C3
HallC2×C11×#3861 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×C3
HallC11×#3861 ⋊ C2×C5
HallC2×C72 ⋊ C3×C11⋊C5
SylowC72 ⋊ C2×C3×C11⋊C5
HallC2×C11 ⋊ C5×#3861
SylowC11 ⋊ C2×C5×#3861

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×#3861
commutator, cosocle, hypocenterC72×C11C2×C3×C5
FrattiniC1G
Fitting, socleC2×C72×C11C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1078

Conjugacy classes & character table

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

Relationships

maximal subgroup of(C11⋊C5)⋊#10596874, C11⋊C5×#10596874, (C11⋊C5)⋊#10596873, …
maximal normal subgroup of(C11⋊C5)⋊#10596874, C11⋊C5×#10596874, (C11⋊C5)⋊#10596873, …
maximal quotient ofC4×C11⋊C5×#3861, C22×C11⋊C5×#3861

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 58);