Finite Group Databasebeta

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C22×C5×C72×C11 #24924742

order10780
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 483840
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C7

Aliases

abelianC22×C5×C72×C11

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10780 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC5×C72×C11×A4, C5×C7×C11×C22⋊ΓL(1,𝔽8), C5×C11×C22⋊#3861, …
socle ofC5×C72×C11×A4, C5×C7×C11×C22⋊ΓL(1,𝔽8), C5×C11×C22⋊#3861, …
maximal subgroup ofC22×C3×C5×C72×C11, C5×C72×C11×A4, C5×C7×C11×C22⋊ΓL(1,𝔽8), …
maximal normal subgroup ofC22×C3×C5×C72×C11, C5×C72×C11×A4, C5×C7×C11×C22⋊ΓL(1,𝔽8), …
maximal quotient ofC22×C3×C5×C72×C11, C2×C5×D3×C72×C11, C2×C4×C5×C72×C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 55);