Finite Group Databasebeta

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C3×(C19⋊C3)⋊Dic53 #49136248

order36252
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C19⋊C3)⋊Dic53
unambiguous semidirect product(C19⋊C3)⋊(C3×Dic53)
unambiguous semidirect productDic1007⋊C32
unambiguous semidirect product(C3×Dic1007)⋊C3

Splittings

derived, HallC19×C53 ⋊ C32×C4
HallC3×C53×C19⋊C3 ⋊ C4
HallDic1007 ⋊ C32
HallC3×C19⋊C3 ⋊ Dic53
SylowC53 ⋊ C3×(C19⋊C3)⋊C4
SylowC19 ⋊ C32×Dic53

Subgroups

subgroupG/H
center, hypercenterC2×C3C53⋊(D19⋊C3)
commutator, hypocenterC19×C53C32×C4
FrattiniC2C3×C53⋊(D19⋊C3)
Fitting, socleC2×C3×C19×C53C2×C3
prime radicalC2×C3×C53×C19⋊C3C2
cosocleC2×C19×C53C2×C32
LCSG ▷ C19×C53
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12084

Conjugacy classes & character table

1458 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36252, 47);