Finite Group Databasebeta

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C2×C3×C4×C8×C25 #72184232

order4800
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 81920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C4×C8×C25
multiplicative(ℤ/9015)ˣ, (ℤ/9616)ˣ, (ℤ/12020)ˣ, (ℤ/18030)ˣ

Subgroups

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

486 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C16×C25, C2×C3×C82×C25, C3×C42×C8×C25, …
maximal normal subgroup ofC2×C3×C4×C16×C25, C2×C3×C82×C25, C3×C42×C8×C25, …
maximal quotient ofC2×C3×C4×C16×C25, C2×C3×C82×C25, C3×C42×C8×C25, …
automorphism group ofC3×C5×C601, C16×C601
outer automorphism group ofC3×C5×C601, C16×C601

GAP

Past the SmallGroups library coverage — no SmallGroups id.