Finite Group Databasebeta

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C2×C5×C27×C41 #72189592

order11070
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C4×C5×C8×C9 (order 2880) · Inn(G) = C1 · Out(G) = C2×C4×C5×C8×C9
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC11070
abelianC2×C5×C27×C41
multiplicative(ℤ/11071)ˣ, (ℤ/22142)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C2×C3×C5×C41
socle, prime radicalC2×C3×C5×C41C9
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11070 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic11070, D22140
maximal subgroup ofC4×C5×C27×C41, C22×C5×C27×C41, C2×D5535, …
maximal normal subgroup ofC4×C5×C27×C41, C22×C5×C27×C41, C2×D5535, …
maximal quotient ofC4×C5×C27×C41, C22×C5×C27×C41
automorphism group ofC11071
outer automorphism group ofC11071

GAP

Past the SmallGroups library coverage — no SmallGroups id.