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Dic21×C71⋊C5 #44447146

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

Aliases

direct productDic21×C71⋊C5
unambiguous semidirect productC3⋊(Dic7×C71⋊C5)
unambiguous semidirect productC7⋊(Dic3×C71⋊C5)
unambiguous semidirect product(C71×Dic21)⋊C5

Splittings

derived, HallC3×C7×C71 ⋊ C4×C5
HallC3×C7×C71⋊C5 ⋊ C4
HallC71×Dic21 ⋊ C5
HallC7×C71⋊C5 ⋊ Dic3
HallC3×C71⋊C5 ⋊ Dic7
HallC7×C71 ⋊ C5×Dic3
HallC3×C71 ⋊ C5×Dic7
SylowC71 ⋊ C5×Dic21
HallC3×C7 ⋊ C4×C71⋊C5
SylowC7 ⋊ Dic3×C71⋊C5
SylowC3 ⋊ Dic7×C71⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D21×C71⋊C5
commutator, hypocenterC3×C7×C71C4×C5
Fitting, socle, cosocleC2×C3×C7×C71C2×C5
prime radicalC2×C3×C7×C71⋊C5C2
LCSG ▷ C3×C7×C71
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5964

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 34);