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C3×C7⋊(Dic71⋊C5) #44447143

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

Aliases

direct productC3×C7⋊(Dic71⋊C5)
unambiguous semidirect product(C71⋊C5)⋊(C3×Dic7)
unambiguous semidirect product(C3×Dic497)⋊C5

Splittings

derived, HallC7×C71 ⋊ C3×C4×C5
HallC3×C7×C71⋊C5 ⋊ C4
HallC3×Dic497 ⋊ C5
HallC7×C71⋊C5 ⋊ C3×C4
HallDic497 ⋊ C3×C5
HallC3×C7×C71 ⋊ C4×C5
HallC3×C71⋊C5 ⋊ Dic7
HallC71⋊C5 ⋊ C3×Dic7
HallC3×C71 ⋊ C5×Dic7
SylowC71 ⋊ C3×C5×Dic7
HallC3×C7 ⋊ Dic71⋊C5
SylowC7 ⋊ C3×Dic71⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C7⋊(D71⋊C5)
commutator, hypocenterC7×C71C3×C4×C5
FrattiniC2C3×C7⋊(D71⋊C5)
Fitting, socleC2×C3×C7×C71C2×C5
prime radicalC2×C3×C7×C71⋊C5C2
cosocleC2×C7×C71C2×C3×C5
LCSG ▷ C7×C71
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5964

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 31);