Finite Group Databasebeta

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C3×C5×Dic3×C179 #44567350

order32220
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C179 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic3×C179
unambiguous semidirect productC3⋊(C3×C4×C5×C179)

Splittings

derivedC3 ⋊ C3×C4×C5×C179
HallC32×C5×C179 ⋊ C4
HallC32×C179 ⋊ C4×C5
HallC32×C5 ⋊ C4×C179
SylowC32 ⋊ C4×C5×C179

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C179D3
commutator, hypocenterC3C3×C4×C5×C179
FrattiniC2C3×C5×D3×C179
Fitting, socle, prime radicalC2×C32×C5×C179C2
cosocleC2×C3C2×C3×C5×C179
LCSG ▷ C3
UCSC1 ◁ C2×C3×C5×C179

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10740

Conjugacy classes & character table

16110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32220, 37);