Finite Group Databasebeta

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C2×C32×C5×C8×C11 #72186829

order7920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 30720
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC2×C32×C5×C8×C11
multiplicative(ℤ/9247)ˣ, (ℤ/11889)ˣ, (ℤ/18494)ˣ, (ℤ/23778)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C32×C5×C11
socle, prime radicalC22×C32×C5×C11C4
LCSG ▷ C1
UCSC1 ◁ G

264 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C32×C5×C11×C16, C32×C4×C5×C8×C11, C22×C32×C5×C8×C11, …
maximal normal subgroup ofC2×C32×C5×C11×C16, C32×C4×C5×C8×C11, C22×C32×C5×C8×C11, …
maximal quotient ofC2×C32×C5×C11×C16, C32×C4×C5×C8×C11, C22×C32×C5×C8×C11, …
automorphism group ofC7×C1321
outer automorphism group ofC7×C1321

GAP

Past the SmallGroups library coverage — no SmallGroups id.