Finite Group Databasebeta

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C4×C5×C8×C17 #72182575

order2720
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8192
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C5×C8×C17
multiplicative(ℤ/3425)ˣ, (ℤ/6850)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C22×C5×C17
socle, prime radicalC22×C5×C17C2×C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2720 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C16×C17, C5×C82×C17, C2×C4×C5×C8×C17, …
maximal normal subgroup ofC4×C5×C16×C17, C5×C82×C17, C2×C4×C5×C8×C17, …
maximal quotient ofC4×C5×C16×C17, C5×C82×C17, C2×C4×C5×C8×C17, …
automorphism group ofC25×C137, C2×C25×C137
outer automorphism group ofC25×C137, C2×C25×C137

GAP

Past the SmallGroups library coverage — no SmallGroups id.