Finite Group Databasebeta

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C7×D7×D31⋊C5 #44477149

order30380
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D7×D31⋊C5
unambiguous semidirect productD31⋊(C5×C7×D7)
unambiguous semidirect product(D7×D31)⋊(C5×C7)
unambiguous semidirect product(C7×D31⋊C5)⋊(C2×C7)
unambiguous semidirect product(D7×ΓL(1,𝔽32))⋊(C2×C7)
unambiguous semidirect product(C7⋊(D31⋊C5))⋊(C2×C7)
unambiguous semidirect product(C7×D7×D31)⋊C5

Splittings

Fitting, socle, HallC72×C31 ⋊ C22×C5
derivedC7×C31 ⋊ C22×C5×C7
HallC72×ΓL(1,𝔽32) ⋊ C22
HallC7×D7×D31 ⋊ C5
HallΓL(1,𝔽32) ⋊ C2×C7×D7
SylowC72 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C5×C7×D7

Subgroups

subgroupG/H
center, hypercenterC7D7×D31⋊C5
commutator, cosocle, hypocenterC7×C31C22×C5×C7
FrattiniC1G
Fitting, socleC72×C31C22×C5
LCSG ▷ C7×C31
UCSC1 ◁ C7

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 434

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 58);