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C7×C3⋊(Dic71⋊C5) #44447145

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

Aliases

direct productC7×C3⋊(Dic71⋊C5)
unambiguous semidirect productC3⋊(C7×Dic71⋊C5)
unambiguous semidirect product(C7×Dic213)⋊C5

Splittings

derived, HallC3×C71 ⋊ C4×C5×C7
HallC3×C7×C71⋊C5 ⋊ C4
HallC7×Dic213 ⋊ C5
HallC7×C71⋊C5 ⋊ Dic3
HallC3×C7×C71 ⋊ C4×C5
HallC3×C71⋊C5 ⋊ C4×C7
HallDic213 ⋊ C5×C7
HallC7×C71 ⋊ C5×Dic3
HallC71⋊C5 ⋊ C7×Dic3
SylowC71 ⋊ C5×C7×Dic3
HallC3×C7 ⋊ Dic71⋊C5
SylowC3 ⋊ C7×Dic71⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(D71⋊C5)
commutator, hypocenterC3×C71C4×C5×C7
FrattiniC2C7×C3⋊(D71⋊C5)
Fitting, socleC2×C3×C7×C71C2×C5
prime radicalC2×C3×C7×C71⋊C5C2
cosocleC2×C3×C71C2×C5×C7
LCSG ▷ C3×C71
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5964

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 33);