Finite Group Databasebeta

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C37×C3⋊(#1039⋊C3) #45686111

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

Aliases

direct productC37×C3⋊(#1039⋊C3)
unambiguous semidirect productC3⋊(C37×#1039⋊C3)
unambiguous semidirect product(C3⋊#1039)⋊(C3×C37)

Splittings

derivedC3×C52 ⋊ C3×C4×C37
HallC3×C37×C52⋊C3 ⋊ C4
HallC52×C37 ⋊ C3×Dic3
HallC3×C52⋊C3 ⋊ C4×C37
SylowC52 ⋊ C3×Dic3×C37

Subgroups

subgroupG/H
center, hypercenterC2×C37C3⋊((C5⋊D5)⋊C3)
commutator, hypocenterC3×C52C3×C4×C37
FrattiniC2C37×C3⋊((C5⋊D5)⋊C3)
Fitting, socleC2×C3×C52×C37C2×C3
prime radicalC2×C3×C37×C52⋊C3C2
cosocleC2×C3×C52C2×C3×C37
LCSG ▷ C3×C52
UCSC1 ◁ C2×C37

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6660

Conjugacy classes & character table

1554 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 384);