Finite Group Databasebeta

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C2×C72×D31⋊C5 #44477154

order30380
automorphism?
homologyAbelianization (H1) = C22×C5×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C72×D31⋊C5
unambiguous semidirect productD31⋊(C2×C5×C72)
unambiguous semidirect product(C2×D31)⋊(C5×C72)
unambiguous semidirect productΓL(1,𝔽32)⋊(C22×C72)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C2×C72)
unambiguous semidirect product(C2×C7×D31)⋊(C5×C7)
unambiguous semidirect product(C2×C72×D31)⋊C5

Splittings

Fitting, socleC2×C72×C31 ⋊ C2×C5
derived, SylowC31 ⋊ C22×C5×C72
HallC72×ΓL(1,𝔽32) ⋊ C22
HallC2×C72×D31 ⋊ C5
HallC72×C31 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C22×C72
HallC2×D31 ⋊ C5×C72

Subgroups

subgroupG/H
center, hypercenterC2×C72D31⋊C5
commutator, cosocle, hypocenterC31C22×C5×C72
FrattiniC1G
Fitting, socleC2×C72×C31C2×C5
LCSG ▷ C31
UCSC1 ◁ C2×C72

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3038

Conjugacy classes & character table

1274 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 63);