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C2×C7×#4294⋊C2 #18012114

order4788
isoclinismisoclinic class of D19⋊C3
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×#4294⋊C2
unambiguous semidirect product#4294⋊(C22×C7)
unambiguous semidirect product(C2×#4294)⋊(C2×C7)

Splittings

derived, SylowC19 ⋊ C22×C7×C9
HallC7×#4294 ⋊ C22
HallC2×C7×D19 ⋊ C9
Hall#4294 ⋊ C22×C7
HallC7×C19 ⋊ C22×C9
HallC2×D19 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D19⋊C3
commutator, hypocenterC19C22×C7×C9
FrattiniC3C2×C7×D19⋊C3
Fitting, socleC2×C3×C7×C19C2×C3
prime radicalC2×C3×C7×D19C3
cosocleC3×C19C22×C3×C7
LCSG ▷ C19
UCSC1 ◁ C2×C3×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2394

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×D5×#4294⋊C2, C2×C5×C7×#4294⋊C2, C2×C7×C5⋊(#4294⋊C2), …
maximal normal subgroup ofC2×C5×C7×#4294⋊C2, C2×C49×#4294⋊C2, C2×C72×#4294⋊C2
maximal quotient ofC7×D5×#4294⋊C2, C2×C5×C7×#4294⋊C2, C2×C7×C5⋊(#4294⋊C2), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 30);