Finite Group Databasebeta

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C3×C7×D901 #49180909

order37842
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D901
unambiguous semidirect productC17⋊(C3×C7×D53)
unambiguous semidirect productC53⋊(C3×C7×D17)

Splittings

Fitting, socle, HallC3×C7×C17×C53 ⋊ C2
derived, HallC17×C53 ⋊ C2×C3×C7
HallC7×C17×C53 ⋊ C2×C3
HallC3×C17×C53 ⋊ C2×C7
HallC3×C7×C53 ⋊ D17
HallC7×C53 ⋊ C3×D17
HallC3×C7×C17 ⋊ D53
HallC3×C53 ⋊ C7×D17
HallC7×C17 ⋊ C3×D53
SylowC53 ⋊ C3×C7×D17
HallC3×C17 ⋊ C7×D53
SylowC17 ⋊ C3×C7×D53

Subgroups

subgroupG/H
center, hypercenterC3×C7D901
commutator, cosocle, hypocenterC17×C53C2×C3×C7
FrattiniC1G
Fitting, socleC3×C7×C17×C53C2
LCSG ▷ C17×C53
UCSC1 ◁ C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18921

Conjugacy classes & character table

9492 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37842, 5);