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C22×C3×C5×C167 #23756607

order10020
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7968
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C3×C5×C167
multiplicative(ℤ/15033)ˣ, (ℤ/20044)ˣ, (ℤ/30066)ˣ

Subgroups

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

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10020 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC5×C22⋊C9×C167, C3×C5×A4×C167
socle ofC22×C5×C9×C167, C5×C22⋊C9×C167, C3×C5×A4×C167
maximal subgroup ofC22×C5×C9×C167, C5×C22⋊C9×C167, C22×C32×C5×C167, …
maximal normal subgroup ofC22×C5×C9×C167, C5×C22⋊C9×C167, C22×C32×C5×C167, …
maximal quotient ofC22×C5×C9×C167, C22×C32×C5×C167, C2×C3×C5×D3×C167, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10020, 9);