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C22×C3×C4×C7×C16 #72184686

order5376
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4718592
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C3×C4×C7×C16
multiplicative(ℤ/10353)ˣ, (ℤ/10965)ˣ, (ℤ/11696)ˣ, (ℤ/11752)ˣ, (ℤ/11865)ˣ, (ℤ/12495)ˣ, (ℤ/12656)ˣ, (ℤ/12992)ˣ, (ℤ/13328)ˣ, (ℤ/13480)ˣ, (ℤ/13760)ˣ, (ℤ/13804)ˣ, (ℤ/14620)ˣ, (ℤ/15680)ˣ, (ℤ/15820)ˣ, (ℤ/16176)ˣ, (ℤ/16272)ˣ, (ℤ/16660)ˣ, (ℤ/16704)ˣ, (ℤ/17628)ˣ, (ℤ/17748)ˣ, (ℤ/20220)ˣ, (ℤ/20340)ˣ, (ℤ/20706)ˣ, (ℤ/21930)ˣ, (ℤ/23730)ˣ, (ℤ/24990)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C24×C3×C7
socle, prime radicalC24×C3×C7C2×C8
LCSG ▷ C1
UCSC1 ◁ G

2044 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5376 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C7×C32, C22×C3×C7×C8×C16, C2×C3×C42×C7×C16, …
maximal normal subgroup ofC22×C3×C4×C7×C32, C22×C3×C7×C8×C16, C2×C3×C42×C7×C16, …
maximal quotient ofC22×C3×C4×C7×C32, C22×C3×C7×C8×C16, C2×C3×C42×C7×C16, …
automorphism group ofC3×C7×C17×C29, C3×C5×C17×C43, C16×C17×C43, …
outer automorphism group ofC3×C7×C17×C29, C3×C5×C17×C43, C16×C17×C43, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.