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C22×C4×C16×C23 #19180946

order5888
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8650752
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C4×C16×C23
multiplicative(ℤ/11985)ˣ, (ℤ/12784)ˣ, (ℤ/15040)ˣ, (ℤ/15980)ˣ, (ℤ/23970)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
FrattiniC2×C8C24×C23
socleC24×C23C2×C8
LCSG ▷ C1
UCSC1 ◁ G

1022 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5888 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C23×C32, C22×C8×C16×C23, C2×C42×C16×C23, …
maximal normal subgroup ofC22×C4×C23×C32, C22×C8×C16×C23, C2×C42×C16×C23, …
maximal quotient ofC22×C4×C23×C32, C22×C8×C16×C23, C2×C42×C16×C23, …
automorphism group ofC3×C5×C17×C47, C16×C17×C47, C5×C47×C64
outer automorphism group ofC3×C5×C17×C47, C16×C17×C47, C5×C47×C64

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5888, 26308);