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C5×C3⋊(Dic71⋊C7) #44447138

order29820
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(Dic71⋊C7)
unambiguous semidirect productC3⋊(C5×Dic71⋊C7)
unambiguous semidirect product(C5×Dic213)⋊C7

Splittings

derived, HallC3×C71 ⋊ C4×C5×C7
HallC3×C5×C71⋊C7 ⋊ C4
HallC5×Dic213 ⋊ C7
HallC5×C71⋊C7 ⋊ Dic3
HallC3×C71⋊C7 ⋊ C4×C5
HallC3×C5×C71 ⋊ C4×C7
HallDic213 ⋊ C5×C7
HallC71⋊C7 ⋊ C5×Dic3
HallC5×C71 ⋊ C7×Dic3
SylowC71 ⋊ C5×C7×Dic3
HallC3×C5 ⋊ Dic71⋊C7
SylowC3 ⋊ C5×Dic71⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(D71⋊C7)
commutator, hypocenterC3×C71C4×C5×C7
FrattiniC2C5×C3⋊(D71⋊C7)
Fitting, socleC2×C3×C5×C71C2×C7
prime radicalC2×C3×C5×C71⋊C7C2
cosocleC2×C3×C71C2×C5×C7
LCSG ▷ C3×C71
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4260

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 26);