Finite Group Databasebeta

← Prev (#30633513) Next (#30633515) →

C2×C11⋊C5×#3862 #30633514

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C7

Aliases

direct productC2×C11⋊C5×#3862
unambiguous semidirect product(C2×C11)⋊(C5×#3862)
unambiguous semidirect product(C2×C11×#3862)⋊C5

Splittings

Fitting, socle, HallC2×C72×C11 ⋊ C3×C5
derived, HallC72×C11 ⋊ C2×C3×C5
HallC2×C72×C11⋊C5 ⋊ C3
HallC2×C11×#3862 ⋊ C5
HallC72×C11⋊C5 ⋊ C2×C3
HallC11×#3862 ⋊ C2×C5
HallC2×C72 ⋊ C3×C11⋊C5
SylowC72 ⋊ C2×C3×C11⋊C5
HallC2×C11 ⋊ C5×#3862
SylowC11 ⋊ C2×C5×#3862

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×#3862
commutator, cosocle, hypocenterC72×C11C2×C3×C5
FrattiniC1G
Fitting, socleC2×C72×C11C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Conjugacy classes & character table

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

Relationships

maximal subgroup of(C11⋊C5)⋊#10596875, C11⋊C5×#10596875, (C11⋊C5)⋊#10596872, …
maximal normal subgroup of(C11⋊C5)⋊#10596875, C11⋊C5×#10596875, (C11⋊C5)⋊#10596872, …
maximal quotient ofC4×C11⋊C5×#3862, C22×C11⋊C5×#3862

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 59);