Finite Group Databasebeta

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C3×C4×C37×C52⋊C3 #45686120

order33300
automorphism?
homologyAbelianization (H1) = C32×C4×C37 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C4×C37×C52⋊C3
unambiguous semidirect product(C4×C52)⋊(C32×C37)
unambiguous semidirect product(C3×C4×C52)⋊(C3×C37)

Splittings

FittingC3×C4×C52×C37 ⋊ C3
derived, SylowC52 ⋊ C32×C4×C37
HallC4×C52×C37 ⋊ C32
HallC52×C37 ⋊ C32×C4
HallC4×C52 ⋊ C32×C37

Subgroups

subgroupG/H
center, hypercenterC3×C4×C37C52⋊C3
commutator, hypocenterC52C32×C4×C37
FrattiniC2C2×C3×C37×C52⋊C3
FittingC3×C4×C52×C37C3
socleC2×C3×C52×C37C2×C3
prime radicalC2×C3×C37×C52⋊C3C2
cosocleC2×C52C2×C32×C37
LCSG ▷ C52
UCSC1 ◁ C3×C4×C37

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6660

Conjugacy classes & character table

4884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 393);