Finite Group Databasebeta

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C23×C3×C4×C169 #72194199

order16224
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6709248
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C4×C169
multiplicative(ℤ/37912)ˣ, (ℤ/48696)ˣ, (ℤ/48744)ˣ, (ℤ/52728)ˣ, (ℤ/56868)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C13C24×C3×C13
socle, prime radicalC24×C3×C13C2×C13
LCSG ▷ C1
UCSC1 ◁ G

708 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16224 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C8×C169, C22×C3×C42×C169, C24×C3×C4×C169
maximal normal subgroup ofC23×C3×C8×C169, C22×C3×C42×C169, C24×C3×C4×C169
maximal quotient ofC23×C3×C8×C169, C22×C3×C42×C169, C24×C3×C4×C169

GAP

Past the SmallGroups library coverage — no SmallGroups id.