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C5×(C31⋊C3)⋊D13 #27130669

order12090
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C31⋊C3)⋊D13

Splittings

Fitting, socle, HallC5×C13×C31 ⋊ C2×C3
derived, HallC13×C31 ⋊ C2×C3×C5
HallC5×C13×C31⋊C3 ⋊ C2
HallC5×D403 ⋊ C3
HallC13×C31⋊C3 ⋊ C2×C5
HallD403 ⋊ C3×C5
HallC5×C31⋊C3 ⋊ D13
HallC5×C31 ⋊ C3×D13
HallC31⋊C3 ⋊ C5×D13
HallC5×C13 ⋊ D31⋊C3
SylowC31 ⋊ C3×C5×D13
SylowC13 ⋊ C5×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC5(C31⋊C3)⋊D13
commutator, cosocle, hypocenterC13×C31C2×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C31C2×C3
LCSG ▷ C13×C31
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

445 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D13×D31⋊C3, D5×(C31⋊C3)⋊D13, (C5⋊(D31⋊C3))⋊D13, …
maximal normal subgroup ofC5×D13×D31⋊C3, D5×(C31⋊C3)⋊D13, (C5⋊(D31⋊C3))⋊D13, …
maximal quotient ofC5×(C31⋊C3)⋊Dic13, C2×C5×(C31⋊C3)⋊D13, C5×(C31⋊C9)⋊D13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12090, 41);