Finite Group Databasebeta

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C22×C3×C4×C11×C31 #72194288

order16368
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 115200
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C11×C31
multiplicative(ℤ/23905)ˣ, (ℤ/25737)ˣ, (ℤ/26637)ˣ, (ℤ/30735)ˣ, (ℤ/32744)ˣ, (ℤ/34316)ˣ, (ℤ/35516)ˣ, (ℤ/47810)ˣ, (ℤ/49116)ˣ, (ℤ/51474)ˣ, (ℤ/53274)ˣ, (ℤ/61470)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C11×C31
socle, prime radicalC23×C3×C11×C31C2
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C8×C11×C31, C2×C3×C42×C11×C31, C23×C3×C4×C11×C31
maximal normal subgroup ofC22×C3×C8×C11×C31, C2×C3×C42×C11×C31, C23×C3×C4×C11×C31
maximal quotient ofC22×C3×C8×C11×C31, C2×C3×C42×C11×C31, C23×C3×C4×C11×C31

GAP

Past the SmallGroups library coverage — no SmallGroups id.