Finite Group Databasebeta

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C5×A4×C179 #24924409

order10740
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C3×C5×C179 · Schur multiplier (H2) = C2

Aliases

direct productC5×A4×C179
unambiguous semidirect productC22⋊(C3×C5×C179)
unambiguous semidirect product(C22×C5)⋊(C3×C179)
unambiguous semidirect product(C22×C179)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C179)⋊C3

Splittings

Fitting, socle, HallC22×C5×C179 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C179
HallC22×C179 ⋊ C3×C5
HallC22×C5 ⋊ C3×C179

Subgroups

subgroupG/H
center, hypercenterC5×C179A4
commutator, cosocle, hypocenterC22C3×C5×C179
FrattiniC1G
Fitting, socleC22×C5×C179C3
LCSG ▷ C22
UCSC1 ◁ C5×C179

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3580 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×A4×C179
maximal normal subgroup ofC3×C5×A4×C179
maximal quotient ofC5×C22⋊C9×C179, C3×C5×A4×C179

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10740, 21);