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C22×C11×C179 #21463517

order7876
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10680
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C11×C179
multiplicative(ℤ/8257)ˣ, (ℤ/16514)ˣ

Subgroups

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

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7876 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC11×A4×C179
socle ofC11×A4×C179
maximal subgroup ofC22×C3×C11×C179, C11×A4×C179, C2×D3×C11×C179, …
maximal normal subgroup ofC22×C3×C11×C179, C11×A4×C179, C2×C4×C11×C179, …
maximal quotient ofC22×C3×C11×C179, C2×D3×C11×C179, C2×C4×C11×C179, …
automorphism group ofC23×C359
outer automorphism group ofC23×C359

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7876, 5);