Finite Group Databasebeta

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C22×C4×C5×C11×C16 #72192241

order14080
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 15728640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C4×C5×C11×C16
multiplicative(ℤ/21505)ˣ, (ℤ/29325)ˣ, (ℤ/30855)ˣ, (ℤ/32912)ˣ, (ℤ/35240)ˣ, (ℤ/36800)ˣ, (ℤ/38720)ˣ, (ℤ/39100)ˣ, (ℤ/41140)ˣ, (ℤ/42288)ˣ, (ℤ/43010)ˣ, (ℤ/52860)ˣ, (ℤ/58650)ˣ, (ℤ/61710)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C24×C5×C11
socle, prime radicalC24×C5×C11C2×C8
LCSG ▷ C1
UCSC1 ◁ G

2044 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 ofC22×C4×C5×C11×C32, C22×C5×C8×C11×C16, C2×C42×C5×C11×C16, …
maximal normal subgroup ofC22×C4×C5×C11×C32, C22×C5×C8×C11×C16, C2×C42×C5×C11×C16, …
maximal quotient ofC22×C4×C5×C11×C32, C22×C5×C8×C11×C16, C2×C42×C5×C11×C16, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.