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C3×(C71⋊C7)⋊Dic5 #44447136

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C71⋊C7)⋊Dic5
unambiguous semidirect product(C71⋊C7)⋊(C3×Dic5)
unambiguous semidirect productDic355⋊(C3×C7)
unambiguous semidirect product(C3×Dic355)⋊C7

Splittings

derived, HallC5×C71 ⋊ C3×C4×C7
HallC3×C5×C71⋊C7 ⋊ C4
HallC3×Dic355 ⋊ C7
HallC5×C71⋊C7 ⋊ C3×C4
HallC3×C71⋊C7 ⋊ Dic5
HallDic355 ⋊ C3×C7
HallC3×C5×C71 ⋊ C4×C7
HallC71⋊C7 ⋊ C3×Dic5
HallC3×C71 ⋊ C7×Dic5
SylowC71 ⋊ C3×C7×Dic5
HallC3×C5 ⋊ Dic71⋊C7
SylowC5 ⋊ C3×Dic71⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D71⋊C7)
commutator, hypocenterC5×C71C3×C4×C7
FrattiniC2C3×C5⋊(D71⋊C7)
Fitting, socleC2×C3×C5×C71C2×C7
prime radicalC2×C3×C5×C71⋊C7C2
cosocleC2×C5×C71C2×C3×C7
LCSG ▷ C5×C71
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4260

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 24);