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C23×C3×C8×C43 #72187192

order8256
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3612672
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C8×C43
multiplicative(ℤ/24792)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C24×C3×C43
socle, prime radicalC24×C3×C43C4
LCSG ▷ C1
UCSC1 ◁ G

676 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8256 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C16×C43, C22×C3×C4×C8×C43, C24×C3×C8×C43, …
maximal normal subgroup ofC23×C3×C16×C43, C22×C3×C4×C8×C43, C24×C3×C8×C43, …
maximal quotient ofC23×C3×C16×C43, C22×C3×C4×C8×C43, C24×C3×C8×C43, …
automorphism group ofC3×C8×C1033
outer automorphism group ofC3×C8×C1033

GAP

Past the SmallGroups library coverage — no SmallGroups id.