Finite Group Databasebeta

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C2×C4×C5×C11×C25 #72189554

order11000
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 160000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C5

Aliases

abelianC2×C4×C5×C11×C25
multiplicative(ℤ/12221)ˣ, (ℤ/15125)ˣ, (ℤ/24442)ˣ, (ℤ/30250)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C5C22×C52×C11
socle, prime radicalC22×C52×C11C2×C5
LCSG ▷ C1
UCSC1 ◁ G

224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C8×C11×C25, C42×C5×C11×C25, C22×C4×C5×C11×C25
maximal normal subgroup ofC2×C5×C8×C11×C25, C42×C5×C11×C25, C22×C4×C5×C11×C25
maximal quotient ofC2×C5×C8×C11×C25, C42×C5×C11×C25, C22×C4×C5×C11×C25
automorphism group ofC121×C125, C2×C121×C125
outer automorphism group ofC121×C125, C2×C121×C125

GAP

Past the SmallGroups library coverage — no SmallGroups id.