Finite Group Databasebeta

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C2×C4×C8×C13×C17 #72192304

order14144
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 393216
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C4×C8×C13×C17
multiplicative(ℤ/21783)ˣ, (ℤ/29044)ˣ, (ℤ/43566)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C23×C13×C17
socle, prime radicalC23×C13×C17C2×C4
LCSG ▷ C1
UCSC1 ◁ G

324 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14144 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C13×C16×C17, C2×C82×C13×C17, C42×C8×C13×C17, …
maximal normal subgroup ofC2×C4×C13×C16×C17, C2×C82×C13×C17, C42×C8×C13×C17, …
maximal quotient ofC2×C4×C13×C16×C17, C2×C82×C13×C17, C42×C8×C13×C17, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.