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C3×C17×Dic177 #49115657

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

Aliases

direct productC3×C17×Dic177
unambiguous semidirect productC3⋊(C3×C17×Dic59)
unambiguous semidirect productC59⋊(C3×Dic3×C17)

Splittings

derivedC3×C59 ⋊ C3×C4×C17
HallC32×C17×C59 ⋊ C4
HallC17×C59 ⋊ C3×Dic3
HallC32×C59 ⋊ C4×C17
HallC32×C17 ⋊ Dic59
SylowC59 ⋊ C3×Dic3×C17
SylowC32 ⋊ C17×Dic59

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D177
commutator, hypocenterC3×C59C3×C4×C17
FrattiniC2C3×C17×D177
Fitting, socle, prime radicalC2×C32×C17×C59C2
cosocleC2×C3×C59C2×C3×C17
LCSG ▷ C3×C59
UCSC1 ◁ C2×C3×C17

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12036

Conjugacy classes & character table

9180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36108, 36);