Finite Group Databasebeta

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C3×C7×Dic71⋊C5 #44447141

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derived, SylowC71 ⋊ C3×C4×C5×C7
HallC3×C7×C71⋊C5 ⋊ C4
HallC3×C7×Dic71 ⋊ C5
HallC7×C71⋊C5 ⋊ C3×C4
HallC7×Dic71 ⋊ C3×C5
HallC3×C7×C71 ⋊ C4×C5
HallC3×C71⋊C5 ⋊ C4×C7
HallC3×Dic71 ⋊ C5×C7
HallC7×C71 ⋊ C3×C4×C5
HallC71⋊C5 ⋊ C3×C4×C7
HallDic71 ⋊ C3×C5×C7
HallC3×C71 ⋊ C4×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D71⋊C5
commutator, hypocenterC71C3×C4×C5×C7
FrattiniC2C3×C7×D71⋊C5
Fitting, socleC2×C3×C7×C71C2×C5
prime radicalC2×C3×C7×C71⋊C5C2
cosocleC2×C71C2×C3×C5×C7
LCSG ▷ C71
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5964

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 29);