Finite Group Databasebeta

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C4×C5×C11×C32 #72186107

order7040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 20480
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C5×C11×C32
multiplicative(ℤ/8825)ˣ, (ℤ/17650)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C16C22×C5×C11
socle, prime radicalC22×C5×C11C2×C16
LCSG ▷ C1
UCSC1 ◁ G

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C11×C64, C5×C8×C11×C32, C2×C4×C5×C11×C32, …
maximal normal subgroup ofC4×C5×C11×C64, C5×C8×C11×C32, C2×C4×C5×C11×C32, …
maximal quotient ofC4×C5×C11×C64, C5×C8×C11×C32, C2×C4×C5×C11×C32, …
automorphism group ofC25×C353
outer automorphism group ofC25×C353

GAP

Past the SmallGroups library coverage — no SmallGroups id.