Finite Group Databasebeta

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C5×Dic3×C71⋊C7 #44447137

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

Aliases

direct productC5×Dic3×C71⋊C7
unambiguous semidirect productC3⋊(C4×C5×C71⋊C7)
unambiguous semidirect product(C5×Dic3×C71)⋊C7

Splittings

derived, HallC3×C71 ⋊ C4×C5×C7
HallC3×C5×C71⋊C7 ⋊ C4
HallC5×Dic3×C71 ⋊ C7
HallC3×C71⋊C7 ⋊ C4×C5
HallC3×C5×C71 ⋊ C4×C7
HallDic3×C71 ⋊ C5×C7
HallC5×C71 ⋊ C7×Dic3
SylowC71 ⋊ C5×C7×Dic3
HallC3×C5 ⋊ C4×C71⋊C7
SylowC3 ⋊ C4×C5×C71⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C5D3×C71⋊C7
commutator, hypocenterC3×C71C4×C5×C7
FrattiniC2C5×D3×C71⋊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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 25);