Finite Group Databasebeta

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C2×C3×C5×#63271 #22551287

order8190
isoclinismisoclinic class of #63271
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×#63271

Splittings

Fitting, socleC2×C3×C5×C7×C13 ⋊ C3
derived, HallC7×C13 ⋊ C2×C32×C5
HallC2×C5×C7×C13 ⋊ C32
HallC5×C7×C13 ⋊ C2×C32
HallC2×C7×C13 ⋊ C32×C5
HallC2×C5×C13 ⋊ C3×ΓL(1,𝔽8)
HallC2×C5×C7 ⋊ C3×C13⋊C3
HallC5×C13 ⋊ C2×C3×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×C13⋊C3
HallC2×C13 ⋊ C3×C5×ΓL(1,𝔽8)
HallC2×C7 ⋊ C3×C5×C13⋊C3
SylowC13 ⋊ C2×C3×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C3×C5×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5#63271
commutator, hypocenterC7×C13C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

990 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×#11763964, C3×C5×#11763962, C3×C5×#11763958, …
maximal normal subgroup ofC3×C5×#11763964, C3×C5×#11763962, C3×C5×#11763958, …
maximal quotient ofC3×C4×C5×#63271, C22×C3×C5×#63271

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 121);