Finite Group Databasebeta

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C4×C5×C11×C37 #22550765

order8140
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C42×C5×C9 (order 2880) · Inn(G) = C1 · Out(G) = C22×C42×C5×C9
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC8140
abelianC4×C5×C11×C37

Subgroups

subgroupG/H
centerGC1
commutatorC1G
FrattiniC2C2×C5×C11×C37
socleC2×C5×C11×C37C2
LCSG ▷ C1
UCSC1 ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8140 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic8140, D16280
Fitting subgroup ofC4×C5×C11×C37⋊C3
maximal subgroup ofC3×C4×C5×C11×C37, C4×C5×C11×C37⋊C3, C5×C11×Dic3×C37, …
maximal normal subgroup ofC3×C4×C5×C11×C37, C4×C5×C11×C37⋊C3, C5×C8×C11×C37, …
maximal quotient ofC3×C4×C5×C11×C37, C5×C11×Dic3×C37, C5×C8×C11×C37, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8140, 1);