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C53×D105 #26013282

order11130
isoclinismisoclinic class of D105
automorphism?
homologyAbelianization (H1) = C2×C53 · Schur multiplier (H2) = C1

Aliases

direct productC53×D105
unambiguous semidirect productC3⋊(C53×D35)
unambiguous semidirect productC5⋊(D21×C53)
unambiguous semidirect productC7⋊(D15×C53)

Splittings

Fitting, socle, HallC3×C5×C7×C53 ⋊ C2
derived, HallC3×C5×C7 ⋊ C2×C53
HallC5×C7×C53 ⋊ D3
HallC3×C7×C53 ⋊ D5
HallC3×C5×C53 ⋊ D7
HallC7×C53 ⋊ D15
HallC5×C53 ⋊ D21
HallC3×C53 ⋊ D35
HallC5×C7 ⋊ D3×C53
HallC3×C7 ⋊ D5×C53
HallC3×C5 ⋊ D7×C53
SylowC7 ⋊ D15×C53
SylowC5 ⋊ D21×C53
SylowC3 ⋊ C53×D35

Subgroups

subgroupG/H
center, hypercenterC53D105
commutator, cosocle, hypocenterC3×C5×C7C2×C53
FrattiniC1G
Fitting, socleC3×C5×C7×C53C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C53

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2862 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD53×D105, D7×D15×C53, D371⋊D15, …
maximal normal subgroup ofD53×D105, D7×D15×C53, D371⋊D15, …
maximal quotient ofC53×Dic105, C2×C53×D105, C53×D315, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11130, 16);