Finite Group Databasebeta

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C22×C4×C52×C13 #72184577

order5200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1105920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C5

Aliases

abelianC22×C4×C52×C13
multiplicative(ℤ/7205)ˣ, (ℤ/9825)ˣ, (ℤ/13100)ˣ, (ℤ/14410)ˣ, (ℤ/19650)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C52×C13
socle, prime radicalC23×C52×C13C2
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C52×C8×C13, C2×C42×C52×C13, C23×C4×C52×C13, …
maximal normal subgroup ofC22×C52×C8×C13, C2×C42×C52×C13, C23×C4×C52×C13, …
maximal quotient ofC22×C52×C8×C13, C2×C42×C52×C13, C23×C4×C52×C13, …
automorphism group ofC5×C11×C131, C3×C25×C131
outer automorphism group ofC5×C11×C131, C3×C25×C131

GAP

Past the SmallGroups library coverage — no SmallGroups id.