Finite Group Databasebeta

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C22×C3×C8×C112 #72190055

order11616
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10137600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C11

Aliases

abelianC22×C3×C8×C112
multiplicative(ℤ/14329)ˣ, (ℤ/17889)ˣ, (ℤ/18423)ˣ, (ℤ/23852)ˣ, (ℤ/28658)ˣ, (ℤ/35778)ˣ, (ℤ/36846)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C3×C112
socle, prime radicalC23×C3×C112C4
LCSG ▷ C1
UCSC1 ◁ G

1064 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C112×C16, C2×C3×C4×C8×C112, C23×C3×C8×C112
maximal normal subgroup ofC22×C3×C112×C16, C2×C3×C4×C8×C112, C23×C3×C8×C112
maximal quotient ofC22×C3×C112×C16, C2×C3×C4×C8×C112, C23×C3×C8×C112
automorphism group ofC7×C23×C89
outer automorphism group ofC7×C23×C89

GAP

Past the SmallGroups library coverage — no SmallGroups id.