Finite Group Databasebeta

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C3×Dic3×C17×C59 #49115658

order36108
automorphism?
homologyAbelianization (H1) = C3×C4×C17×C59 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C17×C59
unambiguous semidirect productC3⋊(C3×C4×C17×C59)

Splittings

derivedC3 ⋊ C3×C4×C17×C59
HallC32×C17×C59 ⋊ C4
HallC32×C59 ⋊ C4×C17
HallC32×C17 ⋊ C4×C59
SylowC32 ⋊ C4×C17×C59

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17×C59D3
commutator, hypocenterC3C3×C4×C17×C59
FrattiniC2C3×D3×C17×C59
Fitting, socle, prime radicalC2×C32×C17×C59C2
cosocleC2×C3C2×C3×C17×C59
LCSG ▷ C3
UCSC1 ◁ C2×C3×C17×C59

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12036

Conjugacy classes & character table

18054 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36108, 37);