Finite Group Databasebeta

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C2×C5×C16×C37 #72185134

order5920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C5×C16×C37
multiplicative(ℤ/6523)ˣ, (ℤ/13046)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C5×C37
socle, prime radicalC22×C5×C37C8
LCSG ▷ C1
UCSC1 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C32×C37, C4×C5×C16×C37, C22×C5×C16×C37, …
maximal normal subgroup ofC2×C5×C32×C37, C4×C5×C16×C37, C22×C5×C16×C37, …
maximal quotient ofC2×C5×C32×C37, C4×C5×C16×C37, C22×C5×C16×C37, …
automorphism group ofC11×C593
outer automorphism group ofC11×C593

GAP

Past the SmallGroups library coverage — no SmallGroups id.