Finite Group Databasebeta

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C23×C5×C8×C23 #72186378

order7360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3784704
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C5×C8×C23
multiplicative(ℤ/15416)ˣ, (ℤ/16544)ˣ, (ℤ/23124)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C24×C5×C23
socle, prime radicalC24×C5×C23C4
LCSG ▷ C1
UCSC1 ◁ G

676 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C5×C16×C23, C24×C5×C8×C23, C22×C4×C5×C8×C23, …
maximal normal subgroup ofC23×C5×C16×C23, C24×C5×C8×C23, C22×C4×C5×C8×C23, …
maximal quotient ofC23×C5×C16×C23, C24×C5×C8×C23, C22×C4×C5×C8×C23, …
automorphism group ofC8×C41×C47, C11×C32×C47
outer automorphism group ofC8×C41×C47, C11×C32×C47

GAP

Past the SmallGroups library coverage — no SmallGroups id.