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C3×C5×Dic553 #45684377

order33180
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic553

Splittings

derived, HallC7×C79 ⋊ C3×C4×C5
HallC3×C5×C7×C79 ⋊ C4
HallC5×C7×C79 ⋊ C3×C4
HallC3×C7×C79 ⋊ C4×C5
HallC3×C5×C79 ⋊ Dic7
HallC5×C79 ⋊ C3×Dic7
HallC3×C79 ⋊ C5×Dic7
HallC3×C5×C7 ⋊ Dic79
SylowC79 ⋊ C3×C5×Dic7
HallC5×C7 ⋊ C3×Dic79
HallC3×C7 ⋊ C5×Dic79
SylowC7 ⋊ C3×C5×Dic79

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D553
commutator, hypocenterC7×C79C3×C4×C5
FrattiniC2C3×C5×D553
Fitting, socle, prime radicalC2×C3×C5×C7×C79C2
cosocleC2×C7×C79C2×C3×C5
LCSG ▷ C7×C79
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33180

Conjugacy classes & character table

8340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 8);