Finite Group Databasebeta

← Prev (#72192104) Next (#72192106) →

C22×C7×C16×C31 #72192105

order13888
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 138240
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C7×C16×C31

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C7×C31
socle, prime radicalC23×C7×C31C8
LCSG ▷ C1
UCSC1 ◁ G

196 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 ofC22×C7×C31×C32, C2×C4×C7×C16×C31, C23×C7×C16×C31
maximal normal subgroup ofC22×C7×C31×C32, C2×C4×C7×C16×C31, C23×C7×C16×C31
maximal quotient ofC22×C7×C31×C32, C2×C4×C7×C16×C31, C23×C7×C16×C31

GAP

Past the SmallGroups library coverage — no SmallGroups id.