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C22×C11×C173 #21439243

order7612
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10320
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C11×C173
multiplicative(ℤ/7981)ˣ, (ℤ/15962)ˣ

Subgroups

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

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7612 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC11×A4×C173, C22×C11⋊C5×C173
socle ofC11×A4×C173, C22×C11⋊C5×C173
maximal subgroup ofC22×C3×C11×C173, C11×A4×C173, C2×D3×C11×C173, …
maximal normal subgroup ofC22×C3×C11×C173, C11×A4×C173, C22×C5×C11×C173, …
maximal quotient ofC22×C3×C11×C173, C2×D3×C11×C173, C22×C5×C11×C173, …
automorphism group ofC23×C347
outer automorphism group ofC23×C347

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7612, 5);