Finite Group Databasebeta

← Prev (#72190077) Next (#72190079) →

C2×C43×C7×C13 #72190078

order11648
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 396361728
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C43

Aliases

abelianC2×C43×C7×C13
multiplicative(ℤ/23055)ˣ, (ℤ/24592)ˣ, (ℤ/30740)ˣ, (ℤ/46110)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23C24×C7×C13
socle, prime radicalC24×C7×C13C23
LCSG ▷ C1
UCSC1 ◁ G

2544 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11648 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C42×C7×C8×C13, C44×C7×C13, C22×C43×C7×C13
maximal normal subgroup ofC2×C42×C7×C8×C13, C44×C7×C13, C22×C43×C7×C13
maximal quotient ofC2×C42×C7×C8×C13, C44×C7×C13, C22×C43×C7×C13
automorphism group ofC16×C29×C53
outer automorphism group ofC16×C29×C53

GAP

Past the SmallGroups library coverage — no SmallGroups id.