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C5×C11⋊#64425 #30633532

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

Aliases

direct productC5×C11⋊#64425

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C2×C3
derived, HallC72×C11 ⋊ C2×C3×C5
HallC5×C11×#3862 ⋊ C2
HallC5×C7⋊D77 ⋊ C3
HallC11×#3862 ⋊ C2×C5
HallC7⋊D77 ⋊ C3×C5
HallC5×#3862 ⋊ D11
HallC5×C72 ⋊ C3×D11
Hall#3862 ⋊ C5×D11
HallC5×C11 ⋊ #64425
SylowC72 ⋊ C3×C5×D11
SylowC11 ⋊ C5×#64425

Subgroups

subgroupG/H
center, hypercenterC5C11⋊#64425
commutator, cosocle, hypocenterC72×C11C2×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C72×C11
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#64418⋊D11, C5×#64422⋊D11, C5×D11×#64425, …
maximal normal subgroup ofC5×#64418⋊D11, C5×#64422⋊D11, C5×D11×#64425, …
maximal quotient ofC5×C11⋊#10596875, C2×C5×C11⋊#64425

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 77);