Finite Group Databasebeta

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C22×C5×#87705 #22547746

order7980
isoclinismisoclinic class of #87705
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×#87705

Splittings

Fitting, socle, HallC22×C5×C7×C19 ⋊ C3
derived, HallC7×C19 ⋊ C22×C3×C5
HallC5×C7×C19 ⋊ C22×C3
HallC22×C7×C19 ⋊ C3×C5
HallC22×C5×C19 ⋊ ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C19⋊C3
HallC5×C19 ⋊ C22×ΓL(1,𝔽8)
HallC22×C19 ⋊ C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C22×C19⋊C3
HallC22×C7 ⋊ C5×C19⋊C3
SylowC19 ⋊ C22×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C22×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC22×C5#87705
commutator, hypocenterC7×C19C22×C3×C5
FrattiniC1G
Fitting, socleC22×C5×C7×C19C3
LCSG ▷ C7×C19
UCSC1 ◁ C22×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

940 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×A4×#87705, C5×#87705⋊A4, C22×C5×ΓL(1,𝔽8)×C19⋊C3, …
maximal normal subgroup ofC5×A4×#87705, C5×#87705⋊A4, C22×C5×ΓL(1,𝔽8)×C19⋊C3, …
maximal quotient ofC22×C5×#11924777, C2×C5×D3×#87705, C22×C3×C5×#87705

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 171);