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C3×Dic13⋊(C52⋊C3) #26043501

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

Aliases

direct productC3×Dic13⋊(C52⋊C3)
unambiguous semidirect product(C3×Dic13)⋊(C52⋊C3)

Splittings

derived, HallC52×C13 ⋊ C32×C4
HallC3×C13⋊(C52⋊C3) ⋊ C4
HallC52×Dic13 ⋊ C32
HallDic13 ⋊ C3×C52⋊C3
SylowC52 ⋊ C3×Dic13⋊C3
SylowC13 ⋊ C3×C4×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D13⋊(C52⋊C3)
commutator, hypocenterC52×C13C32×C4
FrattiniC2C3×D13⋊(C52⋊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

432 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 348);