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C2×C7×(C5⋊D5)⋊C3 #14523622

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

Aliases

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

Splittings

Fitting, socleC2×C52×C7 ⋊ C2×C3
derived, SylowC52 ⋊ C22×C3×C7
HallC2×C7×C5⋊D5 ⋊ C3
HallC7×C52⋊C3 ⋊ C22
HallC52×C7 ⋊ C22×C3
HallC2×C5⋊D5 ⋊ C3×C7
HallC52⋊C3 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52C22×C3×C7
FrattiniC1G
Fitting, socleC2×C52×C7C2×C3
LCSG ▷ C52
UCSC1 ◁ C2×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 210

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C49×(C5⋊D5)⋊C3, C7×D7⋊((C5⋊D5)⋊C3), C7×D7×(C5⋊D5)⋊C3, …
maximal normal subgroup ofC2×C49×(C5⋊D5)⋊C3, C2×C72×(C5⋊D5)⋊C3, C2×C7×C11×(C5⋊D5)⋊C3, …
maximal quotient ofC2×C49×(C5⋊D5)⋊C3, C7×D7⋊((C5⋊D5)⋊C3), C7×D7×(C5⋊D5)⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 102);