Finite Group Databasebeta

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C2×C42×C5×C8×C11 #72192244

order14080
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 251658240
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C43

Aliases

abelianC2×C42×C5×C8×C11
multiplicative(ℤ/35600)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C4C24×C5×C11
socle, prime radicalC24×C5×C11C22×C4
LCSG ▷ C1
UCSC1 ◁ G

4092 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C42×C5×C11×C16, C2×C4×C5×C82×C11, C43×C5×C8×C11, …
maximal normal subgroup ofC2×C42×C5×C11×C16, C2×C4×C5×C82×C11, C43×C5×C8×C11, …
maximal quotient ofC2×C42×C5×C11×C16, C2×C4×C5×C82×C11, C43×C5×C8×C11, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.