Finite Group Databasebeta

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C2×C5×C8×C109 #72187572

order8720
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6912
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C5×C8×C109

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C5×C109
socle, prime radicalC22×C5×C109C4
LCSG ▷ C1
UCSC1 ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C16×C109, C4×C5×C8×C109, C22×C5×C8×C109, …
maximal normal subgroup ofC2×C5×C16×C109, C4×C5×C8×C109, C22×C5×C8×C109, …
maximal quotient ofC2×C5×C16×C109, C4×C5×C8×C109, C22×C5×C8×C109, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.