Finite Group Databasebeta

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C22×C3×C7×C8×C11 #72186398

order7392
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 46080
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C7×C8×C11
multiplicative(ℤ/11481)ˣ, (ℤ/12957)ˣ, (ℤ/13083)ˣ, (ℤ/14816)ˣ, (ℤ/15308)ˣ, (ℤ/17276)ˣ, (ℤ/17444)ˣ, (ℤ/22212)ˣ, (ℤ/22962)ˣ, (ℤ/25914)ˣ, (ℤ/26166)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C3×C7×C11
socle, prime radicalC23×C3×C7×C11C4
LCSG ▷ C1
UCSC1 ◁ G

304 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7392 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C7×C11×C16, C2×C3×C4×C7×C8×C11, C23×C3×C7×C8×C11, …
maximal normal subgroup ofC22×C3×C7×C11×C16, C2×C3×C4×C7×C8×C11, C23×C3×C7×C8×C11, …
maximal quotient ofC22×C3×C7×C11×C16, C2×C3×C4×C7×C8×C11, C23×C3×C7×C8×C11, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.