Finite Group Databasebeta

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C2×C3×C5×C7×D5 #14523675

order2100
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C7×D5
unambiguous semidirect productC5⋊(C22×C3×C5×C7)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C5×C7)

Splittings

Fitting, socleC2×C3×C52×C7 ⋊ C2
derivedC5 ⋊ C22×C3×C5×C7
HallC3×C52×C7 ⋊ C22
HallC52×C7 ⋊ C22×C3
HallC3×C52 ⋊ C22×C7
SylowC52 ⋊ C22×C3×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7D5
commutator, cosocle, hypocenterC5C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C52×C7C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 420

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3×C5×D5×C49, C5×C7×D5×AGL(1,𝔽7), C2×C5×C7×C5⋊AGL(1,𝔽7), …
maximal normal subgroup ofC2×C3×C5×D5×C49, C2×C3×C5×C72×D5, C2×C3×C5×C7×D5×C11, …
maximal quotient ofC2×C3×C5×D5×C49, C5×C7×D5×AGL(1,𝔽7), C2×C5×C7×C5⋊AGL(1,𝔽7), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 155);