Finite Group Databasebeta

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C22×C5×C43⋊C7 #20258232

order6020
isoclinismisoclinic class of C43⋊C7
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C43⋊C7
unambiguous semidirect product(C22×C43)⋊(C5×C7)
unambiguous semidirect product(C22×C5×C43)⋊C7

Splittings

Fitting, socle, HallC22×C5×C43 ⋊ C7
derived, SylowC43 ⋊ C22×C5×C7
HallC5×C43 ⋊ C22×C7
HallC22×C43 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC22×C5C43⋊C7
commutator, hypocenterC43C22×C5×C7
FrattiniC1G
Fitting, socleC22×C5×C43C7
LCSG ▷ C43
UCSC1 ◁ C22×C5

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

260 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×C5×(C43⋊C3)⋊C7, C5×C22⋊((C43⋊C3)⋊C7), C5×A4×C43⋊C7, …
maximal normal subgroup ofC22×C5×(C43⋊C3)⋊C7, C5×C22⋊((C43⋊C3)⋊C7), C5×A4×C43⋊C7, …
maximal quotient ofC2×C5×D3×C43⋊C7, C22×C3×C5×C43⋊C7, C22×C25×C43⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6020, 20);