Finite Group Databasebeta

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C23×C42×C5×C23 #72192829

order14720
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5813305344
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C42×C5×C23
multiplicative(ℤ/41360)ˣ, (ℤ/55320)ˣ, (ℤ/56400)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C25×C5×C23
socle, prime radicalC25×C5×C23C22
LCSG ▷ C1
UCSC1 ◁ G

6000 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C5×C8×C23, C22×C43×C5×C23, C24×C42×C5×C23
maximal normal subgroup ofC23×C4×C5×C8×C23, C22×C43×C5×C23, C24×C42×C5×C23
maximal quotient ofC23×C4×C5×C8×C23, C22×C43×C5×C23, C24×C42×C5×C23

GAP

Past the SmallGroups library coverage — no SmallGroups id.