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C5×C7×Dic237 #45684383

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

Aliases

direct productC5×C7×Dic237
unambiguous semidirect productC3⋊(C5×C7×Dic79)
unambiguous semidirect productC79⋊(C5×C7×Dic3)

Splittings

derived, HallC3×C79 ⋊ C4×C5×C7
HallC3×C5×C7×C79 ⋊ C4
HallC5×C7×C79 ⋊ Dic3
HallC3×C7×C79 ⋊ C4×C5
HallC3×C5×C79 ⋊ C4×C7
HallC7×C79 ⋊ C5×Dic3
HallC5×C79 ⋊ C7×Dic3
HallC3×C5×C7 ⋊ Dic79
SylowC79 ⋊ C5×C7×Dic3
HallC3×C7 ⋊ C5×Dic79
HallC3×C5 ⋊ C7×Dic79
SylowC3 ⋊ C5×C7×Dic79

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D237
commutator, hypocenterC3×C79C4×C5×C7
FrattiniC2C5×C7×D237
Fitting, socle, prime radicalC2×C3×C5×C7×C79C2
cosocleC2×C3×C79C2×C5×C7
LCSG ▷ C3×C79
UCSC1 ◁ C2×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33180

Conjugacy classes & character table

8400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 14);