Finite Group Databasebeta

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C72×C11×A4 #20266409

order6468
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C3×C72×C11 · Schur multiplier (H2) = C2×C7

Aliases

direct productC72×C11×A4
unambiguous semidirect productC22⋊(C3×C72×C11)
unambiguous semidirect product(C22×C11)⋊(C3×C72)

Splittings

Fitting, socle, HallC22×C72×C11 ⋊ C3
derived, SylowC22 ⋊ C3×C72×C11
HallC22×C72 ⋊ C3×C11
HallC22×C11 ⋊ C3×C72

Subgroups

subgroupG/H
center, hypercenterC72×C11A4
commutator, hypocenterC22C3×C72×C11
FrattiniC1G
Fitting, socleC22×C72×C11C3
LCSG ▷ C22
UCSC1 ◁ C72×C11

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C11×A4×ΓL(1,𝔽8), C11×A4×#3861, C11×A4×#3862, …
maximal normal subgroup ofC7×C11×A4×ΓL(1,𝔽8), C11×A4×#3861, C11×A4×#3862, …
maximal quotient ofC72×C11×C22⋊C9, C3×C72×C11×A4, C5×C72×C11×A4

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6468, 144);