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C3×#1039⋊(C13⋊C3) #26043499

order11700
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×#1039⋊(C13⋊C3)
unambiguous semidirect product(C3×#1039)⋊(C13⋊C3)

Splittings

derived, HallC52×C13 ⋊ C32×C4
HallC3×C13⋊(C52⋊C3) ⋊ C4
HallC13×#1039 ⋊ C32
Hall#1039 ⋊ C3×C13⋊C3
SylowC52 ⋊ C3×C4×C13⋊C3
SylowC13 ⋊ C3×#1039⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3(C5⋊D5)⋊(C13⋊C3)
commutator, hypocenterC52×C13C32×C4
FrattiniC2C3×(C5⋊D5)⋊(C13⋊C3)
Fitting, socleC2×C3×C52×C13C2×C3
prime radicalC2×C3×C13⋊(C52⋊C3)C2
cosocleC2×C52×C13C2×C32
LCSG ▷ C52×C13
UCSC1 ◁ C2×C3

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

396 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 346);