Finite Group Databasebeta

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C2×C4×C52×C11 #72182163

order2200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 38400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C5

Aliases

abelianC2×C4×C52×C11
multiplicative(ℤ/3025)ˣ, (ℤ/6050)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C52×C11
socle, prime radicalC22×C52×C11C2
LCSG ▷ C1
UCSC1 ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C52×C8×C11, C42×C52×C11, C22×C4×C52×C11, …
maximal normal subgroup ofC2×C52×C8×C11, C42×C52×C11, C22×C4×C52×C11, …
maximal quotient ofC2×C52×C8×C11, C42×C52×C11, C22×C4×C52×C11, …
automorphism group ofC25×C121, C2×C25×C121
outer automorphism group ofC25×C121, C2×C25×C121

GAP

Past the SmallGroups library coverage — no SmallGroups id.