Finite Group Databasebeta

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C2×C7×C82×C17 #72193252

order15232
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2359296
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C8

Aliases

abelianC2×C7×C82×C17
multiplicative(ℤ/30496)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC42C23×C7×C17
socle, prime radicalC23×C7×C17C42
LCSG ▷ C1
UCSC1 ◁ G

560 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C8×C16×C17, C4×C7×C82×C17, C22×C7×C82×C17
maximal normal subgroup ofC2×C7×C8×C16×C17, C4×C7×C82×C17, C22×C7×C82×C17
maximal quotient ofC2×C7×C8×C16×C17, C4×C7×C82×C17, C22×C7×C82×C17

GAP

Past the SmallGroups library coverage — no SmallGroups id.