Finite Group Databasebeta

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C3×D5×C11×C53 #31775811

order17490
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C53 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5×C11×C53
unambiguous semidirect productC5⋊(C2×C3×C11×C53)

Splittings

Fitting, socle, HallC3×C5×C11×C53 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C11×C53
HallC5×C11×C53 ⋊ C2×C3
HallC3×C5×C53 ⋊ C2×C11
HallC5×C53 ⋊ C2×C3×C11
HallC3×C5×C11 ⋊ C2×C53
HallC5×C11 ⋊ C2×C3×C53
HallC3×C5 ⋊ C2×C11×C53

Subgroups

subgroupG/H
center, hypercenterC3×C11×C53D5
commutator, cosocle, hypocenterC5C2×C3×C11×C53
FrattiniC1G
Fitting, socleC3×C5×C11×C53C2
LCSG ▷ C5
UCSC1 ◁ C3×C11×C53

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8745

Conjugacy classes & character table

6996 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C11×AGL(1,𝔽5)×C53, C3×C11×#11761507, C3×C53×C11⋊AGL(1,𝔽5), …
maximal normal subgroup ofC3×C11×AGL(1,𝔽5)×C53, C3×C11×#11761507, C3×C53×C11⋊AGL(1,𝔽5), …
maximal quotient ofC3×C11×Dic5×C53, C2×C3×D5×C11×C53

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17490, 6);