Finite Group Databasebeta

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C2×C3×D3×C191⋊C5 #46806013

order34380
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D3×C191⋊C5
unambiguous semidirect productC3⋊(C22×C3×C191⋊C5)
unambiguous semidirect product(C2×C3)⋊(C2×C3×C191⋊C5)
unambiguous semidirect product(C2×D3×C191)⋊(C3×C5)
unambiguous semidirect product(C2×C3×D3×C191)⋊C5

Splittings

Fitting, socleC2×C32×C191 ⋊ C2×C5
derivedC3×C191 ⋊ C22×C3×C5
HallC32×C191⋊C5 ⋊ C22
HallC2×C3×D3×C191 ⋊ C5
HallC32×C191 ⋊ C22×C5
SylowC191 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C22×C191⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×C191⋊C5
commutator, cosocle, hypocenterC3×C191C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C191C2×C5
LCSG ▷ C3×C191
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2292

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34380, 68);