Finite Group Databasebeta

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C2×C3×C8×C13×C23 #72192511

order14352
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8448
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C8×C13×C23
multiplicative(ℤ/14711)ˣ, (ℤ/16751)ˣ, (ℤ/21531)ˣ, (ℤ/21537)ˣ, (ℤ/28708)ˣ, (ℤ/29422)ˣ, (ℤ/33502)ˣ, (ℤ/43062)ˣ, (ℤ/43074)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C22×C3×C13×C23
socle, prime radicalC22×C3×C13×C23C4
LCSG ▷ C1
UCSC1 ◁ G

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C13×C16×C23, C3×C4×C8×C13×C23, C22×C3×C8×C13×C23
maximal normal subgroup ofC2×C3×C13×C16×C23, C3×C4×C8×C13×C23, C22×C3×C8×C13×C23
maximal quotient ofC2×C3×C13×C16×C23, C3×C4×C8×C13×C23, C22×C3×C8×C13×C23
automorphism group ofC47×C313, C7×C2393
outer automorphism group ofC47×C313, C7×C2393

GAP

Past the SmallGroups library coverage — no SmallGroups id.