Finite Group Databasebeta

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C22×C4×C11×C31 #72184759

order5456
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 57600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C4×C11×C31
multiplicative(ℤ/10245)ˣ, (ℤ/10928)ˣ, (ℤ/13660)ˣ, (ℤ/20490)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C11×C31
socle, prime radicalC23×C11×C31C2
LCSG ▷ C1
UCSC1 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5456 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C8×C11×C31, C2×C42×C11×C31, C23×C4×C11×C31, …
maximal normal subgroup ofC22×C8×C11×C31, C2×C42×C11×C31, C23×C4×C11×C31, …
maximal quotient ofC22×C8×C11×C31, C2×C42×C11×C31, C23×C4×C11×C31, …
automorphism group ofC3×C5×C683, C16×C683
outer automorphism group ofC3×C5×C683, C16×C683

GAP

Past the SmallGroups library coverage — no SmallGroups id.