Finite Group Databasebeta

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C2×C5×C8×C137 #72189508

order10960
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8704
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C5×C8×C137
multiplicative(ℤ/12067)ˣ, (ℤ/24134)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C5×C137
socle, prime radicalC22×C5×C137C4
LCSG ▷ C1
UCSC1 ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C16×C137, C4×C5×C8×C137, C22×C5×C8×C137
maximal normal subgroup ofC2×C5×C16×C137, C4×C5×C8×C137, C22×C5×C8×C137
maximal quotient ofC2×C5×C16×C137, C4×C5×C8×C137, C22×C5×C8×C137
automorphism group ofC11×C1097
outer automorphism group ofC11×C1097

GAP

Past the SmallGroups library coverage — no SmallGroups id.