Finite Group Databasebeta

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C4×C8×C11×C31 #72189455

order10912
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 38400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C8×C11×C31
multiplicative(ℤ/13645)ˣ, (ℤ/27290)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C22×C11×C31
socle, prime radicalC22×C11×C31C2×C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10912 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C11×C16×C31, C82×C11×C31, C2×C4×C8×C11×C31, …
maximal normal subgroup ofC4×C11×C16×C31, C82×C11×C31, C2×C4×C8×C11×C31, …
maximal quotient ofC4×C11×C16×C31, C82×C11×C31, C2×C4×C8×C11×C31, …
automorphism group ofC5×C2729
outer automorphism group ofC5×C2729

GAP

Past the SmallGroups library coverage — no SmallGroups id.