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C3×C4×C16×C37 #72186155

order7104
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 18432
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC3×C4×C16×C37
multiplicative(ℤ/7709)ˣ, (ℤ/8885)ˣ, (ℤ/15418)ˣ, (ℤ/17770)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C22×C3×C37
socle, prime radicalC22×C3×C37C2×C8
LCSG ▷ C1
UCSC1 ◁ G

116 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7104 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C32×C37, C3×C8×C16×C37, C2×C3×C4×C16×C37, …
maximal normal subgroup ofC3×C4×C32×C37, C3×C8×C16×C37, C2×C3×C4×C16×C37, …
maximal quotient ofC3×C4×C32×C37, C3×C8×C16×C37, C2×C3×C4×C16×C37, …
automorphism group ofC13×C593, C5×C1777
outer automorphism group ofC13×C593, C5×C1777

GAP

Past the SmallGroups library coverage — no SmallGroups id.