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C5×#16838471 #34062094

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#16838471

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derived, HallC72×C13 ⋊ C2×C3×C5
HallC5×C7×#63271 ⋊ C2
HallC5×C13×C7⋊D7 ⋊ C3
HallC7×#63271 ⋊ C2×C5
HallC13×C7⋊D7 ⋊ C3×C5
HallC5×C7⋊D7 ⋊ C13⋊C3
HallC5×C72 ⋊ C2×C13⋊C3
HallC7⋊D7 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ ΓL(1,𝔽8)⋊D7
SylowC72 ⋊ C2×C5×C13⋊C3
SylowC13 ⋊ C5×ΓL(1,𝔽8)⋊D7

Subgroups

subgroupG/H
center, hypercenterC5#16838471
commutator, cosocle, hypocenterC72×C13C2×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C72×C13
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#10587717⋊D7, C5×#10587723⋊D7, C5×D7×#10587721, …
maximal normal subgroup ofC5×#10587717⋊D7, C5×#10587723⋊D7, C5×D7×#10587721, …
maximal quotient ofC5×#21439547, C2×C5×#16838471

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 87);