Finite Group Databasebeta

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C3×C3⋊(Dic191⋊C5) #46805986

order34380
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊(Dic191⋊C5)
unambiguous semidirect productC3⋊(C3×Dic191⋊C5)
unambiguous semidirect product(C191⋊C5)⋊(C3×Dic3)
unambiguous semidirect productDic573⋊(C3×C5)
unambiguous semidirect product(C3×Dic573)⋊C5

Splittings

derivedC3×C191 ⋊ C3×C4×C5
HallC32×C191⋊C5 ⋊ C4
HallC3×Dic573 ⋊ C5
HallC32×C191 ⋊ C4×C5
HallC191⋊C5 ⋊ C3×Dic3
SylowC191 ⋊ C3×C5×Dic3
SylowC32 ⋊ Dic191⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D191⋊C5)
commutator, hypocenterC3×C191C3×C4×C5
FrattiniC2C3×C3⋊(D191⋊C5)
Fitting, socleC2×C32×C191C2×C5
prime radicalC2×C32×C191⋊C5C2
cosocleC2×C3×C191C2×C3×C5
LCSG ▷ C3×C191
UCSC1 ◁ C2×C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2292

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34380, 41);