Finite Group Databasebeta

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C2×C4×C8×C9×C25 #72192558

order14400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 245760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C4×C8×C9×C25
multiplicative(ℤ/22119)ˣ, (ℤ/27015)ˣ, (ℤ/27375)ˣ, (ℤ/28816)ˣ, (ℤ/29492)ˣ, (ℤ/36020)ˣ, (ℤ/36500)ˣ, (ℤ/44238)ˣ, (ℤ/54030)ˣ, (ℤ/54750)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C4×C5C23×C3×C5
socle, prime radicalC23×C3×C5C2×C3×C4×C5
LCSG ▷ C1
UCSC1 ◁ G

729 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C9×C16×C25, C2×C82×C9×C25, C42×C8×C9×C25, …
maximal normal subgroup ofC2×C4×C9×C16×C25, C2×C82×C9×C25, C42×C8×C9×C25, …
maximal quotient ofC2×C4×C9×C16×C25, C2×C82×C9×C25, C42×C8×C9×C25, …
automorphism group ofC3×C73×C125
outer automorphism group ofC3×C73×C125

GAP

Past the SmallGroups library coverage — no SmallGroups id.