Finite Group Databasebeta

← Prev (#21439797) Next (#21439799) →

C2×C3⋊(C7⋊D91) #21439798

order7644
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C3⋊(C7⋊D91)
unambiguous semidirect product(C2×C3)⋊(C7⋊D91)
unambiguous semidirect product(C2×C7)⋊D273
unambiguous semidirect product(C2×C13)⋊(C3⋊(C7⋊D7))

Splittings

Fitting, socleC2×C3×C72×C13 ⋊ C2
derived, HallC3×C72×C13 ⋊ C22
HallC72×C13 ⋊ C2×D3
HallC3×C72 ⋊ C2×D13
SylowC72 ⋊ C2×D39
HallC3×C13 ⋊ C2×C7⋊D7
SylowC13 ⋊ C2×C3⋊(C7⋊D7)
SylowC3 ⋊ C2×C7⋊D91

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C7⋊D91)
commutator, hypocenterC3×C72×C13C22
FrattiniC1G
Fitting, socleC2×C3×C72×C13C2
LCSG ▷ C3×C72×C13
UCSC1 ◁ C2

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1914 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7⋊D819, C2×C3⋊#16838468, C2×C3⋊#16838469, …
maximal normal subgroup ofC2×C3⋊#16838468, C2×C3⋊#16838469, C2×C3⋊(ΓL(1,𝔽8)⋊D91), …
maximal quotient ofC2×C7⋊D819, D3×C3⋊(C7⋊D91), C2×C3×C3⋊(C7⋊D91), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 367);