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C11×C25×C41 #26014762

order11275
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC11275
abelianC11×C25×C41

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C5×C11×C41
socle, prime radicalC5×C11×C41C5
LCSG ▷ C1
UCSC1 ◁ G

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11275 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD11275
Fitting subgroup ofC11×C25×D41, D11×C25×C41, C25×D451, …
maximal subgroup ofC2×C11×C25×C41, C11×C25×D41, D11×C25×C41, …
maximal normal subgroup ofC2×C11×C25×C41, C11×C25×D41, D11×C25×C41, …
maximal quotient ofC2×C11×C25×C41, C3×C11×C25×C41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11275, 1);