Finite Group Databasebeta

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C2×C52⋊C3×D37⋊C3 #45686186

order33300
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC2×C52⋊C3×D37⋊C3
unambiguous semidirect product(C37⋊C3)⋊(C22×C52⋊C3)
unambiguous semidirect product(C2×C37⋊C3)⋊(C2×C52⋊C3)
unambiguous semidirect product(C2×C52×D37⋊C3)⋊C3
unambiguous semidirect product(C2×D37⋊(C52⋊C3))⋊C3
unambiguous semidirect product(C2×D37×C52⋊C3)⋊C3

Splittings

Fitting, socleC2×C52×C37 ⋊ C2×C32
derived, HallC52×C37 ⋊ C22×C32
HallC52⋊C3×C37⋊C3 ⋊ C22
HallC2×C52×D37 ⋊ C32
HallC2×D37 ⋊ C3×C52⋊C3
SylowC37 ⋊ C22×C3×C52⋊C3
SylowC52 ⋊ C2×C3×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C52⋊C3×D37⋊C3
commutator, cosocle, hypocenterC52×C37C22×C32
FrattiniC1G
Fitting, socleC2×C52×C37C2×C32
LCSG ▷ C52×C37
UCSC1 ◁ C2

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1110

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 459);