Finite Group Databasebeta

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C22×C3×C4×C7×C23 #72186649

order7728
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 50688
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C7×C23
multiplicative(ℤ/9541)ˣ, (ℤ/10105)ˣ, (ℤ/11515)ˣ, (ℤ/12093)ˣ, (ℤ/12267)ˣ, (ℤ/14505)ˣ, (ℤ/15464)ˣ, (ℤ/15472)ˣ, (ℤ/16124)ˣ, (ℤ/19082)ˣ, (ℤ/19340)ˣ, (ℤ/20210)ˣ, (ℤ/23030)ˣ, (ℤ/23196)ˣ, (ℤ/24186)ˣ, (ℤ/24534)ˣ, (ℤ/29010)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C7×C23
socle, prime radicalC23×C3×C7×C23C2
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7728 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C7×C8×C23, C2×C3×C42×C7×C23, C23×C3×C4×C7×C23, …
maximal normal subgroup ofC22×C3×C7×C8×C23, C2×C3×C42×C7×C23, C23×C3×C4×C7×C23, …
maximal quotient ofC22×C3×C7×C8×C23, C2×C3×C42×C7×C23, C23×C3×C4×C7×C23, …
automorphism group ofC7×C29×C47, C5×C43×C47
outer automorphism group ofC7×C29×C47, C5×C43×C47

GAP

Past the SmallGroups library coverage — no SmallGroups id.