Finite Group Databasebeta

← Prev (#14523576) Next (#14523578) →

C4×C7⋊(C52⋊C3) #14523577

order2100
isoclinismisoclinic class of C7⋊(C52⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C5

Aliases

direct productC4×C7⋊(C52⋊C3)
unambiguous semidirect product(C4×C7)⋊(C52⋊C3)
unambiguous semidirect product(C4×C52)⋊ΓL(1,𝔽8)

Splittings

Fitting, HallC4×C52×C7 ⋊ C3
derived, HallC52×C7 ⋊ C3×C4
HallC4×C52 ⋊ ΓL(1,𝔽8)
HallC4×C7 ⋊ C52⋊C3
SylowC52 ⋊ C4×ΓL(1,𝔽8)
SylowC7 ⋊ C4×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC4C7⋊(C52⋊C3)
commutator, hypocenterC52×C7C3×C4
FrattiniC2C2×C7⋊(C52⋊C3)
FittingC4×C52×C7C3
socle, cosocleC2×C52×C7C2×C3
prime radicalC2×C7⋊(C52⋊C3)C2
LCSG ▷ C52×C7
UCSC1 ◁ C4

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 420

Conjugacy classes & character table

244 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C52⋊(C49⋊C3), #28413183, #28413184, …
maximal normal subgroup ofC4×C7×C7⋊(C52⋊C3), C4×C11×C7⋊(C52⋊C3), C4×C13×C7⋊(C52⋊C3), …
maximal quotient ofC4×C52⋊(C49⋊C3), #28413183, #28413184, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 57);