Finite Group Databasebeta

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C2×C3×C7×C8×C25 #72187281

order8400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3840
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C7×C8×C25
multiplicative(ℤ/12603)ˣ, (ℤ/16804)ˣ, (ℤ/25206)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C5C22×C3×C5×C7
socle, prime radicalC22×C3×C5×C7C4×C5
LCSG ▷ C1
UCSC1 ◁ G

132 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C7×C16×C25, C3×C4×C7×C8×C25, C22×C3×C7×C8×C25, …
maximal normal subgroup ofC2×C3×C7×C16×C25, C3×C4×C7×C8×C25, C22×C3×C7×C8×C25, …
maximal quotient ofC2×C3×C7×C16×C25, C3×C4×C7×C8×C25, C22×C3×C7×C8×C25, …
automorphism group ofC3×C4201
outer automorphism group ofC3×C4201

GAP

Past the SmallGroups library coverage — no SmallGroups id.