Finite Group Databasebeta

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C2×C5×C7×#63270 #34062178

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C7×#63270

Splittings

Fitting, socle, HallC2×C5×C72×C13 ⋊ C3
derivedC7×C13 ⋊ C2×C3×C5×C7
HallC5×C72×C13 ⋊ C2×C3
HallC2×C72×C13 ⋊ C3×C5
HallC72×C13 ⋊ C2×C3×C5
HallC2×C5×C72 ⋊ C13⋊C3
HallC5×C72 ⋊ C2×C13⋊C3
HallC2×C5×C13 ⋊ C7×ΓL(1,𝔽8)
HallC2×C72 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C2×C7×ΓL(1,𝔽8)
SylowC72 ⋊ C2×C5×C13⋊C3
HallC2×C13 ⋊ C5×C7×ΓL(1,𝔽8)
SylowC13 ⋊ C2×C5×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7#63270
commutator, cosocle, hypocenterC7×C13C2×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C72×C13C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×#11763963, C5×C7×#11763961, C5×C7×#11763957, …
maximal normal subgroup ofC5×C7×#11763963, C5×C7×#11763961, C5×C7×#11763957, …
maximal quotient ofC4×C5×C7×#63270, C22×C5×C7×#63270

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 171);