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C7×D5×#63270 #34062123

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D5×#63270
unambiguous semidirect productC5⋊(C2×C7×#63270)

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derivedC5×C7×C13 ⋊ C2×C3×C7
HallC5×C7×#63270 ⋊ C2
HallC72×D5×C13 ⋊ C3
HallC72×C13 ⋊ C3×D5
HallC72×D5 ⋊ C13⋊C3
HallC5×C72 ⋊ C2×C13⋊C3
HallD5×C13 ⋊ C7×ΓL(1,𝔽8)
HallC5×C13 ⋊ C2×C7×ΓL(1,𝔽8)
SylowC72 ⋊ D5×C13⋊C3
SylowC13 ⋊ C7×D5×ΓL(1,𝔽8)
SylowC5 ⋊ C2×C7×#63270

Subgroups

subgroupG/H
center, hypercenterC7D5×#63270
commutator, cosocle, hypocenterC5×C7×C13C2×C3×C7
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×#19129741, C7×AGL(1,𝔽5)×#63270, C7×#19129729, …
maximal normal subgroup ofC7×#19129741, C7×AGL(1,𝔽5)×#63270, C7×#19129729, …
maximal quotient ofC7×Dic5×#63270, C2×C7×D5×#63270

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 116);