Finite Group Databasebeta

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C2×C4×C7×C8×C31 #72192107

order13888
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 368640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C4×C7×C8×C31

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C23×C7×C31
socle, prime radicalC23×C7×C31C2×C4
LCSG ▷ C1
UCSC1 ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13888 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C7×C16×C31, C2×C7×C82×C31, C42×C7×C8×C31, …
maximal normal subgroup ofC2×C4×C7×C16×C31, C2×C7×C82×C31, C42×C7×C8×C31, …
maximal quotient ofC2×C4×C7×C16×C31, C2×C7×C82×C31, C42×C7×C8×C31, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.