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C4×C5×C7×C79⋊C3 #45684371

order33180
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C7×C79⋊C3
unambiguous semidirect product(C4×C79)⋊(C3×C5×C7)
unambiguous semidirect product(C4×C5×C79)⋊(C3×C7)

Splittings

Fitting, HallC4×C5×C7×C79 ⋊ C3
derived, SylowC79 ⋊ C3×C4×C5×C7
HallC5×C7×C79 ⋊ C3×C4
HallC4×C7×C79 ⋊ C3×C5
HallC4×C5×C79 ⋊ C3×C7
HallC7×C79 ⋊ C3×C4×C5
HallC5×C79 ⋊ C3×C4×C7
HallC4×C79 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC4×C5×C7C79⋊C3
commutator, hypocenterC79C3×C4×C5×C7
FrattiniC2C2×C5×C7×C79⋊C3
FittingC4×C5×C7×C79C3
socleC2×C5×C7×C79C2×C3
prime radicalC2×C5×C7×C79⋊C3C2
cosocleC2×C79C2×C3×C5×C7
LCSG ▷ C79
UCSC1 ◁ C4×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11060

Conjugacy classes & character table

4060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 2);