Finite Group Databasebeta

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C5×C8×C11×C16 #72186108

order7040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 81920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C8

Aliases

abelianC5×C8×C11×C16

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C8C22×C5×C11
socle, prime radicalC22×C5×C11C4×C8
LCSG ▷ C1
UCSC1 ◁ G

208 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C8×C11×C32, C5×C11×C162, C2×C5×C8×C11×C16, …
maximal normal subgroup ofC5×C8×C11×C32, C5×C11×C162, C2×C5×C8×C11×C16, …
maximal quotient ofC5×C8×C11×C32, C5×C11×C162, C2×C5×C8×C11×C16, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.