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C2×C3×D7×C25 #14523554

order2100
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D7×C25

Splittings

FittingC2×C3×C7×C25 ⋊ C2
derived, SylowC7 ⋊ C22×C3×C25
HallC3×C7×C25 ⋊ C22
HallC7×C25 ⋊ C22×C3
HallC3×C7 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D7
commutator, hypocenterC7C22×C3×C25
FrattiniC5C2×C3×C5×D7
FittingC2×C3×C7×C25C2
socleC2×C3×C5×C7C2×C5
prime radicalC2×C3×C5×D7C5
cosocleC5×C7C22×C3×C5
LCSG ▷ C7
UCSC1 ◁ C2×C3×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1050

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3×C25×D49, D7×C25×AGL(1,𝔽7), C2×C25×ΓL(1,𝔽8)⋊D7, …
maximal normal subgroup ofC2×C3×C7×D7×C25, C2×C3×C11×D7×C25, C2×C3×C13×D7×C25, …
maximal quotient ofC2×C3×C25×D49, D7×C25×AGL(1,𝔽7), C2×C25×ΓL(1,𝔽8)⋊D7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 34);