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C7×Dic15×C79 #45684386

order33180
automorphism?
homologyAbelianization (H1) = C4×C7×C79 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic15×C79
unambiguous semidirect productC3⋊(C7×Dic5×C79)

Splittings

derived, HallC3×C5 ⋊ C4×C7×C79
HallC3×C5×C7×C79 ⋊ C4
HallC5×C7×C79 ⋊ Dic3
HallC3×C7×C79 ⋊ Dic5
HallC3×C5×C79 ⋊ C4×C7
HallC5×C79 ⋊ C7×Dic3
HallC3×C79 ⋊ C7×Dic5
HallC3×C5×C7 ⋊ C4×C79
HallC5×C7 ⋊ Dic3×C79
HallC3×C7 ⋊ Dic5×C79
SylowC5 ⋊ C7×Dic3×C79
SylowC3 ⋊ C7×Dic5×C79

Subgroups

subgroupG/H
center, hypercenterC2×C7×C79D15
commutator, hypocenterC3×C5C4×C7×C79
FrattiniC2C7×D15×C79
Fitting, socle, prime radicalC2×C3×C5×C7×C79C2
cosocleC2×C3×C5C2×C7×C79
LCSG ▷ C3×C5
UCSC1 ◁ C2×C7×C79

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33180

Conjugacy classes & character table

9954 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 17);