Finite Group Databasebeta

← Prev (#44477154) Next (#44477156) →

C2×C7×C7⋊(D31⋊C5) #44477155

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

Aliases

direct productC2×C7×C7⋊(D31⋊C5)
unambiguous semidirect product(C2×C7)⋊(C7×D31⋊C5)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C7×D7)
unambiguous semidirect product(C2×D217)⋊(C5×C7)
unambiguous semidirect product(C2×C7×D217)⋊C5

Splittings

Fitting, socleC2×C72×C31 ⋊ C2×C5
derivedC7×C31 ⋊ C22×C5×C7
HallC72×ΓL(1,𝔽32) ⋊ C22
HallC2×C7×D217 ⋊ C5
HallC72×C31 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C2×C7×D7
SylowC72 ⋊ C2×D31⋊C5
SylowC31 ⋊ C2×C5×C7×D7

Subgroups

subgroupG/H
center, hypercenterC2×C7C7⋊(D31⋊C5)
commutator, cosocle, hypocenterC7×C31C22×C5×C7
FrattiniC1G
Fitting, socleC2×C72×C31C2×C5
LCSG ▷ C7×C31
UCSC1 ◁ C2×C7

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 868

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 64);